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UC  SOUTHERN  REGIONAL  LIBRARY  FACILITY 

1    III!  llllil 

4 

\D  BOOK 


UCSB   LIBRARY;  ^^ 

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■  rtE  PROPERTY  Ci 

mu 


ENOINEEH'S 


I^IELD      BOOK 


BY 

C.  S.  CROSS,  CIVIL  ENGINEER 

TO  WHICH  ARE  ADDED  SEVEN  CHAPTERS  ON 

RAILROAD   LOCATION   AND    CONSTRUCTION. 

COMPILED  AND  EDITED  BY 

GEO.  H.  FROST,  C.  E. 


if'OXjRTia:  EDiTioisr. 


NEW  YORK : 
ENGINEERING  NEWS  PUBLISHING  CO., 

1893. 


Copyright,  1893,  by 
ENGINEERING  NEWS  PUBLISHING  COMPANY. 


CONTENTS. 


CHAPTER  I. 


Pages. 

Cross'  Engineer's  Field  Book 5-44 

Bailroad  Curves,  5.  Radius  and  Degree  of  Curve,  6.  Examples,  7. 
Deflection  from  Tangents,  8.  Field  Notes  for  a  Two-degree  Curve,  9. 
Field  Notes  for  a  Three-degree  Curve,  11.  Reverse  Curves,  13.  Com- 
pound Curves,  14.  Formulas,  17.  Railroad  Curve  Tables,  18-27. 
Table  for  Converting  Minutes  and  Seconds  to  Decimals  of  a  Degree, 
28.  Curve  Table,  29-30.  Field  Notes  of  a  Survey,  31.  Prismoidal 
Formula,  32.  Field  Notes  for  Sections,  34.  Computation  of  Earth- 
work, .35.  Excavation  and  Embankment  Tables,  37-43.  Charles  S. 
Cross,  44. 

CHAPTER  II. 

Smith's  Engineering  Field  Work 45-64 

Preliminary  Organization  of  Field  Party,  46.  Care  of  Men,  47.  The 
Transitman,  47.  The  Leveller,  49,  The  Head  Chainman,  50.  The 
Rear  Chainman,  52.  Location,  .53,  The  Topographer,  54.  Keeping 
Transit  Notes,  55,  Compound  Curves,  58.  Land  Lines,  59.  Preserv- 
ing the  Lines,  60.  Centers  and  Grades,  61.  Culverts  and  Masonry, 
62.    Earthwork  Measurement,  62.    Responsibility  of  an  Engineer,  63. 

CHAPTER  in. 

Shunk's  Regulations  During  Construction 65-85 

Organization,  65.  Preparatory  Work,  66.  Right  of  Way,  68.  Final 
Preparations  for  Construction,  69.  Structure  Plans,  70.  Field  and 
Office  Records,  71.  Inspectors  and  Timekeepers,  76.  Estimates,  77, 
Accounts,  Supplies  and  Sundries,  78.  Miscellaneous  Instructions 
and  Suggestions,  79.  Barnes'  Instructions  relative  to  Field  Notes, 
85. 

CHAPTER   IV. 

Topography  and  Staking-out  Problems 86-102 

Table  for  Computing  Right  of  Way  Areas,  86,  Topographical  Field 
Work,  87.  Method  of  Locating  Contours,  87.  Field  Notes,  88.  Field 
Plotting,  89.  Locating  Buildings,  89.  Methods  of  Setting  Slope 
Stakes,  90.  I.  For  Level  Sections,  90.  II,  For  Irregular  Sections, 
90.  III.  With  a  Patent  Tape,  92.  IV.  By  Computation  from  Form- 
ulas, 93.  Flattening  a  Curve,  94.  Le  Baron's  Methods  for  Staking- 
out  Switches,  95.    Metric  Railway  Curves,  98. 


4  CONTENTS. 

CHAPTER    V, 

Transition  or  Easement  Curves  103-117 

The  Tapering  Curve,  103.  The  Railroad  Spiral,  104.  The  Pennsylvania 
Method,  104.  The  Transition  Spiral,  105.  Spalding's  Location  of  the 
Cubic  Parabola,  106.  Location  by  Ordinates,  107.  Location  by  Deflec- 
tion Angles,  109.  Special  Cases,  113.  Table  of  Ordinates  for  Locating 
the  Cubic  Parabola,  114.  Table  of  Deflections  for  Locating  the  Cubic 
Parabola,  115.  Table  for  Corrections,  116.  Elevation  of  the  Outer 
Rail,  116. 

CHAPTER    VL 

Earthwork  and  Masonry 118- 130 

Fisher's  Method  of  Estimating  Overhaul  in  Earthwork,  118.  1.  Compi- 
lation of  Data,  119.  2.  Plotting  the  Profile,  120.  Taking  off  the  Re- 
sults, 121.  Expansion  of  Rock  in  Embankment,  122.  Specht's  Notes 
on  Earthwork,  122.  Wellington's  Rules  for  Earthwork  Computation, 
121.  Levee  Construction,  125.  Specifications  for  Masonry,  126.  Brick 
for  Buildings  and  for  Arches,  127.  Rubble,  127.  Squared  Stone  Ma- 
sonry, 128.    Ashlar  Masonry,  129. 

CHAPTER  VII. 

Culverts  and  Bridges 131-145 

Standard  Timber  Box  Culverts,  131.  Low's  Formula  and  Tables  for 
Maximum  Spans  of  Box  Culverts,  135.  Specifications  for  Stone  Box 
Culverts,  136.  Specifications  for  Arch  Culverts,  137.  Howe  Truss 
Bridges,  139.  Cost  of  Labor  in  Framing  and  Erecting  a  Howe  Truss 
Bridge,  143.  Howe  Trusses  on  Canadian  Pacific  Railway,  144.  For- 
mulas for  the  Weights  of  Bridges,  145. 

CHAPTER  VIIL 

Construction  Details 146-159 

Centers  for  Arches,  146.  Ri^pairs  to  the  Arch  of  the  Musconetcong  Tun- 
nel, 150.  Standard  Fences  and  Gates  on  Canadian  Pacific  Railway, 
153.  Substructure  for  a  Water  Tank,  154.  A  Pile  Driving  Machine, 
with  two  Plates,  155.  Age  of  Railroads  in  Different  Countries,  158. 
Rules  for  Measuring  Work,  159.  Directions  for  Making  Drawings  for 
Reproduction,  159. 

APPENDIX. 

Books  for  Railroad  Engineers 160-165 

Mathematics.  Surveying.  Drawing.  Mechanics.  Astronomy  and 
Geodesy.    Bridges  and  Roofs.     Construction.    Hydraulics. 


THl 


PCRTY  Of 


m  w, 


CHAPTER   I. 


Cross'  Engineers  Field   Book. 

RAILROAD    CURVES. 

The  following  tables  show  the  distance  from  the  point  of  inter- 
section of  the  tangent  lines  to  the  beginning  of  a  one  degree  curve, 
the  angle  of  deflection  (=angle  at  centre)  being  known. 

In  the  columns,  under  the  head  of  degrees  and  opposite  the  min- 
utes, are  given  the  distances  in  feet  from  the  intersection  of  tan- 
gents to  the  beginning  of  one  degree  curve. 

To  ascertain  the  distance  for  any  given  degree  of  curve,  divide 
the  distance  given  in  the  tables  for  a  One  degree  curve,  by  the 
degrees  of  the  required  curve,  and  you  have  the  distance  from  the 
point  of  intersection  to  the  beginning  or  end  of  curve. 

EXAMPLE: 

Eequired  the  distance  from  the  point  of  intersection  of  tangents 
to  the  beginning  of  a  Two  degrees  curve,  the  angle  of  deflection 
being  25°. 

In  the  tables  under  25°,  and  opposite  0',  And  1270.28  which  divided 
by  the  degrees  of  the  curve  (2°)  give  635.14  feet  the  required  dis- 
tance. 

In  staking  the  centre  line  for  a  railroad  or  a  canal,  stakes  should 
be  driven  down  to  near  the  surface  of  the  ground,  at  the  intersec- 
tion of  the  tangents,  and  at  the  different  stations ;  and  nails  set  in 
indicating  the  centre  point.  These  stakes  serve  also  for  leveling 
purposes  and  are  useful  in  detecting  errors  while  the  work  is  being 
relevelled  and  stak^  d  out. 


6  RAILROAD    CURVES. 

The  beginning  and  end  of  curves  should  have  reference  stakes 
set  at  right  angle  to  the  centre  line,  similarly  driven  and  marked, 
and  at  such  convenient  distance  from  the  centre  as  will  insure  them 
from  being  displaced  in  making  excavations  and  embankments; 
and  at  all  the  above  named  points  another  stake  for  numbering, 
&c.,  should  be  firmly  driven  adjacent  to  them. 

The  radius  of  a  One  degree  curve  is  5730  feet.  The  circle  being 
divided  into  360  parts  of  one  degree  (equal  angle  of  deflection)  give 
360  chords  of  one  foot  in  length  at  the  circumference,  and  also  a 
radius  of  57.3  ft.  thus : 

360  114.6 


3.U16  2 

The  choud  of  One  foot  in  length  for  1  degree  =    57.3  ft.  Radius. 
"  10    feet  "  "      ••       =   573.0 

100      "  "  "       "       =5730.0 

Or  the  radius  may  be  calculated  by  natural  sines,  thus : 

sin.  1°:  100  ft.  chord  :   :  sin.  89°  30'   :  5730  ft.  radius. 

To  determine  the  degree  of  curvature,  having  the  radius  given, 
divide  the  radius  of  a  One  degree  curve,  5730,  by  the  radius  of  the 
given  curve. 

EXAMPLE : 

Required  the  degree  of  a  curve  having  a  radius  oi  lOOO  feet : 

Uto  =  5.73°  =  5°  43'  48" 

To  determine  the  length  of  the  curve  having  the  angle  of  deflec- 
tion given  :  divide  the  angle  of  deflection  (=angle  at  centre)  by  the 
degrees  of  the  curve,  and  you  have  the  required  length  of  the  curve. 
If  there  are  degrees  and  minutes  in  the  angle  of  deflection,  the  min- 
utes should  be  converted  into  decimals. 

EXAMPLE : 

The  angle  of  deflection  being  20°  49',  |g  =0.816.  Then  20.816  is  the 
distance  for  a  One  degree  curve  ;  if  for  a  2  degrees  curve,  divide  this 
result  by  2 ;  for  a  3  degrees  curve,  divide  by  three,  and  so  on. 

The  angle  of  deflection  being  given,  the  following  results  are 
readily  determined : 


RAILROAD    CURVES. 


Angle 

of 

deflection 

Degree 

of 
curve 

Deflection 

per 
100  feet. 

Radius 

of 
curve 

Dist.  from 

intersec.  to 

beginning 

of  (;urve. 

Length 
curve. 

20°  49' 

1° 

0°30' 

5730. 

1052.49 

2081.6 

20"  49' 

2° 

1°00' 

2865. 

526.24 

1040.8 

20'  49' 

3° 

1°30' 

1910. 

350.83 

693.8 

20'  49' 

4° 

2' 00' 

1432.5 

263.12 

520.4 

20°  49' 

5° 

2°  30' 

1146. 

210.50 

416.3 

To  ascertain  the  radius  .of  a  curve,  having  the  angle  of  deflection, 
and  the  distance  from  intersection  to  beginning  of  curve  given. 
Find  the  distance  for  the  angle  of  deflection  in  the  tables,  which 
divided  by  5730.  gives  the  natural  tangent  of  half  the  angle. 

Then  divide  the  distance  from  intersection  to  beginning  of  curve 
by  the  natural  tangent  of  half  the  angle,  and  you  have  the  radius. 

EXAMPLE : 

Required  the  Radius  of  a  curve,  the  angle  of  deflection  being  20°, 
and  the  distance  from  interst^ction  of  tangents  to  beginning  of 
curve  225  feet. 

Under  20°  and  opposite  0'  in  the  tables,  find  1010.37,  which  divided 
by  5730  feet  gives  the  natural  tangent  0.17633.  Then  225  ft.  divided 
by  0.17633  gives  the  radius  1276  feet. 

FlEIiD  NOTES  FOB  A  OnB  DEOBEE  CUBVE. 


Bearing  of  1st  tangent N.  20°  W. 

2d.       ■  "        N.  40°W. 

Angle  of  deflection  by  needle 20° 

"  **  "  graduated  card    ...    20° 


The  angles  measured  with  the  card  are  the  most  reliable ;  but 
the  angles  by  the  needle  although  it  often  indicates  a  slight  differ- 


8 


RAILROAD    CURVES. 


ence,  serves  as  a  check  to  greater  errors  which  may  arise  in  reading 
the  degrees  on  the  graduated  limb  of  the  instrument. 
*  Station  No.  506.2000    Intersection  of  tangents. 

—  10.1037    from  intersection  to  beginning  of  curve. 


•  Station  No.  496,0963    point  at  wliich  curve  commences. 
+   20.0000    length  of  curve. 


*  Station  No.  516.0963    point  at  which  curve  terminates. 


DEFLECTION  FBOM  TANQENTS. 


Length  of 

Deflection 

Stations. 

chords 

from 

REMARKS. 

in  feet. 

tangent. 

496.096 

<(    >( 

H          <( 

*  Beginning  of  curve. 

497. 

90.37 

0^    27 

1=  to  left.  cTang.  due  N.) 

498. 

100.00 

0^    57 

499. 

100.00 

1^   27 

500. 

100.00 

1'    57 

501. 

100.00 

2"    27 

502. 

100.00 

2°    57 

Change  point. 

503. 

100.00 

3=    27 

504. 

100.00 

3'"    57 

505. 

100.00 

4^    27 

506. 

100.00 

4=    57 

507. 

100.00 

5'    27 

508. 

100.00 

5^    57 

509. 

100.00 

6'^    27 

*  Change  point. 

510. 

100.00 

6^    57 

511. 

100.00 

7"    27 

512. 

100.00 

7'    57 

513. 

100.00 

8"    27 

514. 

100.00 

8"    57 

515. 

100.00 

9'    27 

516. 

100.00 

9"    57 

516.0963 

9.63 

10"    00 

*  End  of  curve. 

(Tangent  N.  20°  W.) 

RAILEOAD    CURVES. 

FIELD  NOTES  FOR  A  TWO  DEGBEES  CURVE. 

Bearing  of  1st  tangent N   10°  W. 

2d  '•    N   30°  W. 

Angle  of  deflection  by  needle 20° 

'*  "       by  graduated  card 20° 

Station . . .    506.200  intersection  of  tangents. 

—     5.052  from  do.  to  beginning  of  curve. 


Station —  501.148  point  at  which  the  curve  commences. 
+  10.000  length  of  the  curve. 


Station —  511,148  point  at  which  the  curve  terminates. 


DEFLECTION  FROM  TANGENTS. 


Stations. 

Length  of 

chords  in 

feet. 

Deflection 
from  tangent. 

REMARKS. 

501.148 

»>         " 

0=     00' 

*  Beginning  of  curve  2°  to  left. 

502. 

85.20 

0°     51 

(Tangent  N  10°  W.) 

503. 

100.00 

1°     51 

504. 

100.00 

2°    51 

505. 

100.00 

3°    51 

506. 

100.00 

4°    51 

507. 

100.00 

5°    51 

*  Change  point. 

508. 

100.00 

6^    51 

m 

509. 

100.00 

T    51 

510. 

100.00 

8°    51 

511. 

100.00 

9°     51 

511.148 

14.80 

10°    00 

*  End  of  curve. 

(Tangent  N  30°  W. 


10  EAILKOAD    CUKVES, 

In  curves  of  great  length,  the  instrument  should  be  moved  for- 
ward in  about  every  five  or  six  hundred  feet  to  insure  accuracy, 
and  often  to  avoid  obstruction  in  line.  The  mode  of  pr.)ceeding  in 
such  cases  may  be  illustrated  with  the  deflections  of  the  2""  curve. 

The  instrument  in  the  first  place  is  set  at  station  501.148  and  the 
deflection  from  tangent  to  station  507  is  5°  51'.  Now  change  the 
position  of  the  instrument  to  station  507,  and  bring  the  cross  hairs 
to  bear  on  the  staff  at  station  501.148;  after  clamping  the  instru- 
ment turn  with  the  vernier  as  a  test 

for  station  502,  0°51' 

for      "       503,  1°51' 

for      "       504,  2=51' 

for      "        505,  3°51' 

and  for  the  tangential  station  507,  5°51'    *  Ch.pt. 

If  the  stakes  are  found  to  be  correct,  continue  the  setl  ing  of  the 
remaining  stakes  to  end  of  curve,  and  deflect  the  degrees  from  the 
beginning  of  curve  given  in  the  field  notes  opposite  the  respective 
stations. 

When  an  odd  number  of  minutes  are  to  be  turned  off  at  the 
commencement  and  for  each  successive  station,  the  inconvenience 
may  be  obviated  by  setting  the  vernier  the  number  of  minutes  for 
the  required  chord  in  an  opposite  direction  from  that  in  which  you 
would  turn  for  the  stations  in  the  curve ;  or  so  that  the  instrument 
when  set  in  line  with  the  tangent  and  clamped,  the  nonius  instead 
of  reading  0,  will  indicate  the  number  of  degrees  or  minutes  which 
would  be  deflected  to  strike  in  line  with  the  first  stake  to  be  set 
in  the  curve.  Then  the  remainder  of  the  stations  will  be  free  from 
the  odd  minutes  which  would  otherwise  be  turned  off  for  each 
successive  station. 

When  the  instrument  is  moved  forward  to  another  station,  the 
same  mode  maybe  adopted  with  reference  to  setting  the  nonius 
preparatory  to  bringing  the  cross  hairs  to  bear  on  the  staff  at  the 
beginning  of  curve. 

By  determining  the  tangents  at  the  various  points  in  the  curve 
over  which  the  instrument  may  be  set,  the  staking  of  the  curve 
may  be  prosecuted  with  less  liability  to  error. 


EAILROAD    CURVES. 


11 


At  the  end  of  curve  the  instrument  should  be  set  over  the  stake 
to  ascertain  if  the  tangent  produced  from  deflection  corresponds 
with  the  course  and  direction  of  the  tangential  line. 

Field  Notes  and  method  of  staking  a  3  '  Curve. 

Bearing  of  1st  tangent,  N.  20^^  W. 
2d         '^         N.  40"  W. 
Angle  of  deflection  by  needle  20". 
"  "by  graduated  card  20^. 


*    Station 


*    Station 


.  506.180    intersection  of  tangents. 

—     3.368    from  do.         do.  to  beginning  of  curve. 


.  502.812    point  at  which  the  curve  commences, 
-f-     6.666    length  of  curve. 


Station  .    .  509.478    point  at  which  the  curve  terminates. 


The  notes  are  put  down  as  represented  in  this  diagram,  and 
numbered  from  right  to  left  when  curving  to  the  left,  and  from 
left  to  right  when  curving  to  the  right. 


12 


KAILROAD    CURVES. 
FIELD    NOTES. 


No.  of 
Station 


502.812 

503. 

504. 

505. 

506. 

507. 

508. 

509. 

509.478 

510. 


I  Length 
I       of 
;  chords. 


Course  of      jDeflect'nl 

tangents  from    i 

and  chords,      tangent. 


REMARKS. 


18.8 

100 

100 

100 

100 

100 

100 
47.8 
52.2 


N  20°  W 

20  17' 

22.  04 

25.  04 

28.  04 

31.  04 

34.  04 

37   04 

29.04 
N   40   00  W 


0° 

0' 

i    0" 

17' 

1. 

47 

1     3. 

17 

4. 

47 

6. 

17 

7. 

47 

9. 

17 

10. 

00 

*  B.  C.  r  to  left. 

*  Change  point. 

'  E.  C. 


The  number  at  which  the  curve  ends  should  be  given  to  the 
chainman  before  proceeding  to  measurement,  so  that  the  prefer 
signal  may  be  made  by  him  on  arriving  at  the  station  next  preced- 
ing the  termination  of  the  curve. 

Then  set  the  instrument  over  the  point  of  curve  at  station  502.812 
and  deflect  from  the  tangent  line  for  station    503,  0-  17' 

504,  1-  47' 

505,  33  17' 

and  so  on  to  the  end  of  curve  as  per  column  of  deflection,  unless 
the  instrument  is  moved  forward.  If  it  is  necessary  to  move  the 
instrument,  then  set  it  over  another  stake  in  the  curve,  bring  the 
cross  hairs  to  bear  on  the  staff  at  the  beginning  of  curve  and 
clamp  the  instrument;  then  turn  off  for  the  tangent  at  the  sta- 
tion selected,  the  same  number  of  degrees  originally  turned  from 
tangent  at  beginning  of  curve  in  setting  the  stake,  and  1  30'  addi- 
tional for  each  successive  station  of  100  feet  as  you  advance ;  the 
angles  should  correspond  with  those  given  in  the  column  of  deflec- 
tions set  opposite  the  resi)ective  stations. 

It  frequently  occurs  that  the  instrument  has  to  be  changed  to 
points  intermediate  between  two  stations. 

If  in  a  five  degrees  curve,  for  instance,  it  is  necessary  to  change 
the  instrument  from  station  No.  0,  there  being  an  obstruction  in 


BAJLROAD    CURVES.  13 

the  line  of  sight  between  station  0  and  station  No.  3.  and  nothing 
to  prevent  the  instrument  being  set  over  a  point  in  the  curve  30 
feet  distant  from  station  2;  the  deflections  would  be  made  as 
follows : 

Station    0    Deflection  =  0°  00  B.  C.  5°  R. 
1  "  2°  30. 

"2  "  5°  00. 

2.30      "  5°  45.  *    Change  point. 

Then  move  the  instrument  forward,  and  set  it  over  station  2.30, 
and  bring  the  cross  hairs  to  bear  on  the  staff  at  the  beginning  of 
the  curve,  station  0;  then  turn  off  5°  45'  for  tangent  at  station 
2.30  and  1°  45'  for  70  feet  the  remainder  of  station  No.  3,  making 
in  all  for  station  No  3 — deflections  7°  30' 

4  "  10°  00' 

5  "  15°  00'  E.  C. 

The  angles  for  parts  of  a  station  on  curves  may  be  readily  calcu- 
lated and  the  angles  turned  off  in  such  manner  as  will  keep  the 
stations  of  uniform  length  throughout  the  line. 

REVERSE  CURVES. 

These  may  be  put  in  according  to  the  formation  of  the  ground 
with  equal  radii,  or  not,  as  the  case  may  require.  In  the  latter 
case  the  degree  of  curve  may  be  assumed  and  the  curve  continued 
as  far  as  deemed  necessary ;  and  the  tangent  is  then  produced  to 
the  intersection  and  measured— and  the  angle  of  deflection  de- 
termined. These  give  the  data  from  which  the  radius  and  degree 
of  curve  are  determined. — See  Pages  6  and  7. 

In  the  former  case  select  a  point  in  one  of  the  tangents  and  turn 
from  tangent  such  angle  as  the  case  may  require,  and  measure  on 
this  line  the  distance  between  the  tangents.  Then  set  in  a  point 
one  half  of  this  distance  for  the  point  of  reversion,  from  which  both 
curves  may  be  staked  ont.—See  Pages  6  and  7. 

If  you  wish  to  compound  a  curve  so  that  the  trains  will  pass  less 
abruptly  from  tangent  into  and  through  the  curve,  it  may  be 
done  in  the  following  manner : 


14 


BAILBOAD    CURVES. 


We  will  assume  the  angle  of  deflection  to  be  40° ;  in  the  tables 
under  40°  and  opposite  0'  find  2085.55,  the  distance  from  intersec- 
tion of  tangents  to  beginning  of  a  one  degree  curve. 

If  you  wish  to  lay  out  a  compound  equivalent  to  a  curve  of  5° 
for  the  whole  angle,  divide  the  distance  found  (2085.55)  by  5,  de- 
gree of  the  curve ;  and  you  have  the  point  of  beginning  417  ft.  from 
intersection  of  tangents.  You  will  then  decide  on  what  length  to 
substitute  the  less  degree  of  curve. 

Tf  a  3°  curve  is  decided  on,  and  the  distance  200  feet  at  each  end 
of  the  5°  curve,  then  deduct  3°  for  each  station  of  100  feet,  making 


KAILEOAD    CUKVES, 


16 


12°  from  the  total  angle  of  deflection,  (40°)  and  you  have  28°  to  be 
divided  equally  between  the  stations  of  the  intermediate  curve,  or 
ZB  _  70^  ^jjg  required  degree  of  curve. 

FIELD  NOTES. 


No.  of 
Station. 


Course  of 
chords. 


Deflection. 


EEMARKS. 


No  0. 
1 
2 
3 
4 
5 
6 
7 


<c 

(< 

Nl° 

30' 

w 

4 

30 

9 

30 

16 

30 

28 

30 

30 

30 

35 

30 

38 

30 

0°  00' 
1°  30' 
3  00 
3  30 
7  00 
10  30 
14  00 
1  30 
3     00 


Beginning  of  curve, 

End  of  curve,  3°,  B.  C.  7° 
From  tangent. 


E.  C.  7°,  B.  C.  3°. 
From  tangent. 

E.  C.  3°. 

Tangent,  N  40°  W. 


NATURAL  TANGENTS. 

From  the  tables  may  also  be  determined  the  natural  tangent  for 
any  given  number  of  degrees  and  minutes  from  one  degree  to  45°, 
by  taking  the  distance  given  in  the  tables  for  twice  the  angle  of 
which  the  tangent  is  sought,  and  dividing  the  same  by  5730. 

EXAMPLES  : 

1st.  Required  the  natural  tangent  of  30°.  Under  60°  (twice  the 
angle)  find  in  the  tables  3308.21  and  divide  the  same  by  5730,  and 
you  have  the  natural  tangent  for  30°  =  0.57735. 


2d.    Required  the  natural  tangent  for  an  angle  of  7°  28';  in  the 


16  BAILEOAp    CURyES. 

column  of  distances  under  14°  and  opposite  56'  (twice  the  angle)  find 
750,97,  which  divided  by  5730  give  the  natural  tangent  for  7°  28' 
equal  to  0.13106. 

MEASUREMENT    WITH    GUNTER'S    CHAIN. 

When  a  66  feet  chain  is  used  for  the  length  of  stations,  the  radius 
of  a  one  degree  curve.  5730  feet,  may  represent  57.30  chains  of  66 
feet,  and  the  distances  in  the  tables  applied  the  same  as  for  chains 
of  100  feet  in  length ;  but  the  radius  as  well  as  the  length  of  sta- 
tions will  be  proportionally  less  than  for  stations  of  100  feet  in 
length  by  .^^  part. 

If  a  66  feet  chain  is  used,  the  distance  after  being  found  in  the 
tables,  may  be  divided  by  66,  and  the  stations  in  the  curve  reduced 
to  75.76  links  which  are  equal  to  50  feet,  one  half  the  length  of 
the  stations  generally  adopted  in  btaking  the  center  line  of  rail- 
roads ;  and  the  curve  staked  out  accordingly,  turning  off  one  half 
the  number  of  degrees  required  for  the  stations  of  100  feet  in 
length. 

The  degree  of  curvature  is  understood  to  express  the  number  of 
degrees  per  100  feet,  and  hence  the  convenience  of  making  the  sta- 
tions of  such  length  as  will  give  a  definite  idea  of  the  degree  of 
curve  and  length  of  radius. 


The  following  abbreinaiions  ore  used  by  some  Engineers. 

P.  C.        For  Point  of  Curve,  or  Beginning  of  Curve. 
P.  T.  "        "      "    Tangent,  or  End  of  Curve. 

P.  C.  C.  "  "  "  Compound  Curve — or  end  of  one  curve  and 
beginning  of  another,  curving  in  the  same 
direction. 

P.  B.  C.  "  '■'  '■  Reverse  Curve,  or  point  where  the  direction 
of  the  curve  is  changed  from  right  to  left, 
or  vice  versa. 

P.  I.  "        "      "    Intersection  of  Tangents. 


RAILROAD  CURVES. 


17 


[Values  of  the  radius  corresponding  to  different  degrees  of  curve  are 
shown  in  the  following  table: 


Degree. 

Radius. 

Degree. 

Radius. 

Degree. 

Radius. 

0°  30' 

11459.2 

6°  30' 

881.95 

13" 

441.63 

1 

5729.6 

7 

819.02 

14 

410.27 

1    30 

3819.8 

7    30 

764.49 

15 

383.06 

2 

2864.9 

8 

716.78 

16 

359.27 

2    30 

2292.0 

8    30 

674,69 

17 

338.27 

3 

1910. 1 

9 

637  27 

18 

319  62 

3    30 

1637.3 

9    30 

603.81 

19 

302.94 

i 

1432.7 

10 

573.69 

20 

287.94 

i    30 

1273.6 

10    30 

546.44 

2^ 

231.01 

5 

1146.3 

11 

521.67 

30 

193.18 

5    30 

1042.1 

11    30 

499.06 

35 

166.28 

6 

955.4 

12 

478.^4 

40 

146.19 

Let  I  be  the  angle  of  inclination  between  the  two  tangents,  d  the  de- 
gree of  the  curve,  R  its  radius,  and  T  the  distance  from  P.  I.  to  P.  C.  or 
P.  r.    Then  the  following  formulas  may  be  used  to  give  accurate  results: 

50 


For  the  radius 


R  = 


sin  i  d 

For  the  tangent  distance  T  =  R  tan  i  I. 
These  formulas  will  often  be  needed  in  the  field  for  curves  of  over  6 
degrees.  For  instance,  when  I  =  20°  and  d  =  10°,  the  rule  of  page  6 
gives  R  =  573,0  feet  and  page  20  gives  T  =  101.04  feet,  wliile  the  accu- 
rate formulas  give  R  =  573.69  feet  and  T  =  101.16  feet.  If  d  is  assumed 
and  I  is  given,  the  value  of  T  may  be  found,  without  computing  the 
radus,  from  the  formula 

sin  i  1 1 
and  this  in  general  must  be  used  in  careful  location,  particularly  when- 
ever d  is  greater  than  five  or  six  degrees. — The  Editor.] 


18 


RAILROAD  CURVE  TABLES. 

1 

0° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

; 

0 

0.00 

50.02 

101.00 

160.07 

200.09 

260.17 

300.30 

350.44 

400.70 

0 

1 

0.83 

50.85 

100.83 

160.90 

200.92 

251.00 

301.14 

351.28 

401.54 

1 

2 

1.67 

51.69 

101.67 

151.74 

201.76 

261.84 

301.97 

352.11 

402.37 

2 

3 

2.50 

52.52 

102.50 

152.57 

202.59 

252.67 

302.80 

3.52.95 

403.21 

3 

4 

3.33 

53.35 

103.34 

153.41 

203.43 

253.51 

303.64 

353.79 

404.05 

4 

5 

4.17 

54.18 

104.17 

164.24 

204.26 

254.34 

304.47 

354.62 

404.88 

5 

6 

6.00 

55.02 

105.01 

155.08 

205.10 

255.18 

305.31 

35.5.46 

405.72 

6 

7 

5.83 

55.85 

105.84 

156.91 

205.93 

256.01 

306.14 

356.30 

406.65 

7 

8 

6.67 

56.68 

106.68 

156.75 

206.77 

256.85 

306.98 

357.13 

407.39 

8 

9 

7.50 

57.52 

107.51 

167.68 

207.60 

257.68 

307.81 

367.97 

408.23 

9 

10 

8.33 

58.35 

108.35 

158.42 

208.44 

258.52 

308.65 

358.81 

409.06 

10 

11 

9.17 

59.18 

109.18 

159.26 

209.27 

259.35 

309.48 

359.64 

409.90 

11 

12 

10.00 

60.01 

110.02 

160.09 

210.11 

260.20 

310.32 

360.48 

410.74 

12 

13 

10.83 

60.85 

110.85 

160.92 

210.94 

261.03 

311.15 

361.32 

411.57 

13 

14 

11.67 

61.68 

111.69 

161.76 

211.77 

261.86 

311.99 

362.15 

412.41 

14 

16 

12.50 

62.52 

112.52 

16-2.59 

212.61 

262.70 

312.83 

362.99 

413.25 

15 

16 

13.33 

63.35 

113.36 

163.43 

213.45 

263.54 

313.66 

363.K3 

414.08 

16 

17 

14.17 

64.18 

114.19 

161.26 

214.28 

264.37 

314.49 

364.66 

414.92 

17 

18 

15.00 

65.01 

115.02 

165.09 

216.11 

265.20 

315.33 

365.50 

415.75 

18 

19 

15.83 

65.86 

115.86 

165.93 

215.95 

266.04 

316.16 

366.34 

416.59 

19 

20 

16.67 

66.68 

116.69 

166.76 

216.78 

266.87 

317.00 

367.17 

417.43 

20 

21 

17.50 

67.51 

117.53 

167.60 

2x7.62 

267.71 

317.84 

368.01 

418.26 

21 

22 

18.3:3 

68.36 

118.36 

168.43 

218.45 

268.54 

318.67 

368.86 

419.10 

22 

23 

19.17 

69.18 

119.20 

169.27 

219.29 

269.38 

319.  .50 

369.68 

419.94 

23 

24 

20.00 

70.01 

120.03 

170.10 

220.12 

270.21 

320.34 

370.52 

420.77 

24 

1    25 

20.83 

70.85 

120.87 

170.94 

220  96 

271.(» 

321.18 

371.36 

421.61 

25 

26 

21.67 

71.68 

121.70 

171.77 

•22179 

271.88 

322.01 

372.19 

422.45 

26 

27 

22.50 

72.61 

122.54 

172.61 

222.63 

272.72 

32-2.H5 

373.03 

423.28 

27 

i    28 

23.33 

73.34 

123.37 

173.44 

223.46 

273.64 

323.68 

373.86 

424.12 

28 

29 

24.17 

74.18 

124.21 

174.28 

224.30 

274.38 

324.52 

374.70 

424.96 

29 

1    30 

25  00 

75.01 

125.03 

175.10 

225.13 

275.21 

326.35 

375  64 

425.79 

30 

31 

25.83 

75.84 

126.87 

175.88 

225.96 

276.05 

326.19 

376.38 

426.63 

31 

1    32 

26.67 

76.68 

126.70 

176.72 

226.80 

276.88 

327.04 

377.22 

427.47 

32 

33 

27.50 

77.51 

127.53 

177.55 

227.63 

277.72 

327.86 

378.05 

428.31 

33 

:    34 

28.33 

^8.34 

128.37 

178.39 

228  47 

278.55 

328.69 

378.89 

429.15 

34 

1    35 

29.17 

79.17 

129.20 

179.22 

229.30 

279.39 

329.53 

379.73 

429.98 

35 

,    36 

30.00 

80.01 

130.04 

180.06 

230.14 

280.23 

330.37 

380.67 

430.8-2 

36 

1    37 

30.83 

80.84 

130.87 

180.89 

230.97 

281.06 

331.20 

381.41 

431.66 

37 

38 

31.67 

81.67 

131.71 

181.73 

231.81 

281.90 

332.04 

382.24 

432.50 

38 

i    39 

32.50 

82.51 

132.64 

182.56 

232.64 

282.73 

332.87 

383.08 

433.34 

39 

1    40 

33.33 

83.34 

133.38 

183.40 

233.48 

283.57 

333.71 

383.92 

434.18 

40 

'    41 

34.17 

84.17 

134.21 

184.23 

234.31 

284.41 

334.55 

384.76 

435.02 

41 

1    42 

35.00 

85.01 

135.05 

185.07 

235.16 

285.24 

335.38 

385.60 

435.86 

42 

I    43 

35.83 

85.84 

135.88 

185.90 

235.98 

286.08 

336.22 

386.43 

436.70 

43 

1    44 

36.66 

86.67 

136.72 

186.74 

236.82 

286.91 

337.05 

387.27 

437.54 

44 

45 

37.50 

87.51 

137.66 

187.57 

237.65 

287.75 

.337.89 

388.11 

438.37 

45 

46 

38.33 

88.34 

ISH..'^ 

188.40 

"238.48 

288.59 

338.73 

3H8.96 

439.21 

46 

47 

39.17 

89.17 

139.22 

189.24 

239.32 

289.42 

339.56 

389.79 

440.05 

47 

48 

40.00 

90.00 

140.05 

190.07 

240.15 

290.26 

340.40 

390.62 

440.89 

48 

49 

40.83 

90.84 

140.89 

190.91 

240.99 

291.09 

341.23 

391.46 

441.73 

49 

60 

41.67 

91.67 

141  72 

191.74 

241.82 

291.93 

342.07 

392.30 

442.57 

50 

51 

42.50 

92.50 

142.56 

192.58 

242.66 

292.77 

342.91 

393.14 

443.41 

51 

62 

43.33 

93.34 

143.39 

193.41 

243.49 

293.60 

343.74 

393.98 

444.25 

52 

53 

44.17 

94-17 

144.23 

194.25 

244.33 

294.44 

344.58 

394.81 

445.09 

53 

64 

45.00 

95.00 

145.06 

195.08 

245.16 

295.27 

345.41 

395.66 

445.93 

54 

55 

45.83 

95.84 

145.90 

195,92 

246.00 

296.11 

346.25 

396.49 

446.76 

55 

56 

46.fi7 

9ii.67 

146.73 

196.75 

246.  a3 

296.95 

347.08 

397.33 

447.60 

56 

57 

47.50 

97.50 

147.57 

197.59 

247.67 

297.78 

347.92 

398.17 

448.44 

57 

58 

48.33 

98.33 

148.40 

198.42 

248.50 

298.62 

348.76 

399.01 

449.28 

58 

69 

49.17 

99.17 

149.24 

199.26 

249.34 

299.46 

349.60 

399.85 

460.12    69 

19 


RAILROAD  CURVE  TABLES. 

/ 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

r 

0 

450.95 

501.32 

.5.51.74 

602.2'2 

652.87 

703.53 

754.35 

805.29 

856.35 

0 

1 

451.79 

502.16 

,552.58 

603.06 

653.71 

704.38 

7.55.20 

806.14 

857.20 

1 

2 

452.63 

f03.00 

553.42 

603,91 

654.56 

705.23 

766  05 

806.99 

858.05 

2 

3 

453.47 

503. H4 

554.26 

604.75 

655.40 

706.07 

756. K9 

807.84 

858.90 

3 

i 

454.31 

504.68 

5.55.10 

605.60 

656.25 

706.92 

757.74 

808.64 

859.76 

4 

5 

455.14 

505.52 

555.94 

606.44 

657.09 

707.77 

7,58.69 

809.54 

860.61 

5 

6 

455.98 

506.36 

5.56.78 

607.28 

657.93 

708.62 

759.44 

810.39 

861.46 

6 

7 

456.82 

507.10 

557.62 

608.13 

658.78 

709.47 

760.29 

811.24 

862.31 

7 

8 

457.66 

508.04 

5.-18.46 

608.97 

659.62 

710.31 

761.13 

81-2.09 

863.16 

8 

9 

458.50 

508.88 

569.30 

609.82 

()60.47 

711.16 

761.98 

812.94 

864.01 

9 

10 

4.^9.34 

.509.72 

.560.14 

610.66 

661.31 

712.01 

762.83 

813.79 

864.87 

10 

11 

466.18 

510  56 

560.98 

611.50 

662  15 

712.86 

763.68 

814.64 

865.72 

11 

12 

461.02 

511.40 

561.82 

612.35 

663.00 

713.71 

7t;4.53 

815.49 

866.57 

12 

13 

461.86 

512.24 

562.66 

613.19 

663.84 

714.65 

765.37 

816.34 

867.42 

13 

U 

462.70 

513.08 

563.50 

614.04 

664.69 

715.40 

766.22 

817.19 

868.27 

14 

15 

463.53 

513.92 

564.. 34 

614.88 

665.63 

716.25 

767.07 

818.04 

869.12 

15 

16 

464.37 

514.76 

665.18 

615.72 

666.37 

717.10 

767.92 

818.89 

869.98 

16 

17 

465.21 

515.60 

566.02 

616.57 

667.22 

717.95 

768.77 

819.74 

870.83 

17 

18 

466.05 

516.44 

566.86 

617.41 

668.06 

718.79 

769.61 

820  59 

871.68 

18 

19 

466.89 

517.28 

567.70 

618.26 

668.91 

719,64 

770.46 

821.44 

872.53 

19 

20 

467.73 

518.12 

568.54 

619.10 

669.76 

720.49 

771.31 

822  29 

873.38 

20 

21 

468.57 

518.96 

569.38 

619.94 

670.59 

721. .35 

77-2.16 

823.14 

874.23 

21 

22 

469.41 

519  80 

670.22 

620.79 

671.44 

722.20 

773.01 

823  99 

876.09 

22 

23 

470.26 

520.64 

571.06 

621.63 

672.28 

723.04 

773.K5 

824.84 

.  876.94 

23 

24 

471.08 

521.48 

571.90 

622.48 

673.13 

723.89 

774.70 

825  69 

876.79 

24 

25 

471.92 

522.32 

572.74 

623.32 

673.97 

724.74 

776.55 

826.54 

877.64 

25 

26 

472.76 

523.16 

673.58 

624.16 

674.81 

725.59 

776.40 

8-27.39 

878.49 

26 

27 

473.60 

5-24.01 

574.42 

625.01 

675.66 

726.44 

777.35 

828.24 

879.34 

27 

28 

474.43 

524.85 

575.27 

625.85 

676.51 

727.28 

778.09 

829  09 

880.20 

28 

29 

475.26 

525.69 

576.  U 

626.70 

677.35 

728.13 

778.94 

829.94 

881.05 

29 

30 

476.10 

526.53 

676.96 

627.55 

678.20 

728.97 

779.79 

830.79 

881.90 

30 

31 

476.94 

527.37 

677.79 

628.39 

679.04 

729.82 

780.64 

831.64 

882.75 

31 

32 

477.78 

528.21 

578.63 

629.24 

679.89 

730.66 

781.49 

832.49 

883.61 

32 

33 

478.62 

529.05 

579.48 

630.08 

680.73 

731.51 

782.34 

833.35 

884.46 

33 

34 

479.46 

529.89 

580.32 

630.93 

681.58 

732.35 

783.19 

834.20 

885.32 

34 

35 

480.30 

530.73 

581.16 

631.77 

682.42 

733.20 

784.04 

835.05 

886.17 

35 

36 

481.14 

531.57 

582.00 

6.32.61 

683.26 

734.05 

784.89 

835.90 

887.02 

36 

37 

481.99 

532.41 

582.84 

633  46 

684.11 

734.89 

785.74 

836.75 

887.88 

37 

38 

482.83 

533.25 

583.69 

634.30 

684.95 

7.35.74 

786.59 

837.61 

888.73 

38 

39 

483.67 

534.09 

584.53 

635.15 

685.80 

736.58 

787.44 

838.46 

889.59 

39 

40 

484.51 

534.93 

586.37 

636.99 

686.64 

737.43 

788. -29 

839.31 

890.44 

40 

41 

485.35 

535.77 

586.21 

636.83 

687.48' 

738.28 

789.14 

840.16 

891.29 

41 

42 

486.19 

536.61 

587.05 

637.68 

688.33 

7.39.12 

789.99 

841.01 

89-J.15 

42 

43 

487.03 

537.45 

587.90 

638.52 

689.17 

739.97 

790.84 

841.87 

893.00 

43 

44 

487.87 

538.29 

588.74 

639..37 

690.02 

740.81 

791.69 

842.72 

893.86 

44 

45 

488.71 

539.  l.i 

589.58 

640.21 

690.86 

741.66 

792.54 

813.57 

894.71 

45 

46 

489  56 

539.97 

590.42 

641.05 

691.70 

742.51 

793.39 

844.42 

895.56 

46 

47 

490.40 

540.81 

.591.26 

641.90 

692.55 

743.35 

794.24 

845.27 

896.42 

47 

48 

491.24 

541.65 

592.11 

642.74 

693.39 

744.20 

796.09 

846.13 

897.27 

48 

49 

492.08 

542.49 

592.95 

643.59 

694.24 

745.04 

795.94 

846.98 

898.13 

49 

50 

492.92 

543.33 

593.79 

644.43 

695.08 

745.89 

796.79 

847.83 

898.98 

60 

51 

493.76 

544.17 

694.63 

646.27 

696.92 

746.74 

797.64 

848.68 

899.83 

51 

52 

494.60 

545.01 

595.47 

646.12 

696.77 

747..58 

798.49 

849.53 

900.69 

62 

63 

495.44 

545.85 

596.32 

646.96 

697.61 

748.43 

799.34 

850.39 

901.54 

53 

54 

496.28 

546.69 

597.16 

647.81 

698.46 

749.27 

800.19 

851.24 

902.40 

54 

55 

497.12 

547.53 

598.00 

648.65 

699.30 

750.12 

801.04 

852.09 

903.25 

56 

58 

497.96 

548.37 

598.84 

649.49 

700.14 

750.97 

801.89 

8,52.94 

904.10 

56 

57 

498.  Hi 

549.21 

599.68 

650.34 

700.99 

751.81 

802.74 

H53.79 

901.96 

67 

58 

499.65 

550.06 

600.63 

651.18 

701.83 

752.66 

803.59 

851.65  1 

905.81 

58 

59 

600.48 

550.90 

601.38 

652.03 

702.68 

753.50 

801.44 

855.50  ; 

906.67 

59 

20 


RAILROAD  CURVE  TABLES. 

/ 

18° 

19°    1     20^          21°    1    22°    1     23°    |    2-1°    |     25°    |     26°    |  ' 

0 

007.52 

958.86    1010.37    1062.00  ;  1113.80  :  1165.76    1217.96    1270.28  i  1322.88 

0 

1 

908.38 

959.72 

1011.23 

1062.86 

1114.67 

1166.63 

1218.83 

1271.16 

13-23.76 

1 

3 

90J.23 

960.57 

1012.09 

1063.73 

1115.53 

1167.50 

1210.70 

1-272.03 

1324.63 

2 

3 

910.09 

961.43 

1012.95 

1064.59 

1116.40 

1168.37 

1220.57 

1-272.91 

1325.51 

3 

4 

910.94 

%2.30 

1013.81 

1065.45 

1117.26 

1169.24 

1221.45 

1273.79 

13-26.39 

4 

5 

911.80 

963.15 

1014.67 

1066.32 

1118,13 

1170.11 

1222.32 

1-274.66 

1327.27 

6 

6 

912.65 

964.00 

1015.53 

1067.18 

1118.99 

1170.98 

1223.19 

1-275.54 

13-28.14 

6 

7 

913.51 

964.86 

1016.39 

1068.04 

1119.86 

1171.85 

1224.06 

1276.42 

1329.02 

7 

8 

914.36 

965.72 

1017.24 

1068.91 

1120.72 

1172.71 

1224.93 

1277.-29 

13-29.90 

8 

9 

915.22 

966.58 

1018.10 

1069.77 

1121.59 

1173.58 

1225.80 

1278.17 

1330.78 

9 

10 

916.07 

967.43 

1018.96 

1070.63 

1122.45 

1174.45 

1226.67 

1279.05 

1331.65 

10 

11 

916.93 

968.29 

1019.82 

1071.50 

1123.32 

1175.32 

1227.54 

1-279.92 

1332.53 

11 

13 

917.78 

969.15 

10-20.68 

1072.36 

1124.18 

1176.19 

1228.42 

1-280.80 

13:J3.41 

12 

13 

918.64 

970.00 

1021.54 

1073.22 

1125.05 

1177.06 

1229.29 

1281.69 

1334.28 

13 

14 

919.49 

970.86 

1022.40 

1074.09 

ir25,91 

1177.93 

1230.16 

1282.55 

1335.16 

14 

15 

920.35 

971.72 

1023.26 

1074.95 

1126.78 

1178.80 

1-231.03 

1-283.43 

1336.04 

15 

16 

921.20 

972.58 

1024.12 

1075.81 

1127.64 

1179.67 

1231.90 

1284.31 

1336.92 

16 

17 

922.06 

973.43 

1024.98 

1076.68 

1128.50 

1180.54 

1232.77 

1285.18 

1337.79 

17 

18 

922.91 

974.29 

1025.84 

1077.54 

1129.37 

1181.41 

1233.64 

1286.06 

1338.67 

18 

19 

923.77 

975.15 

1026.70 

1078.40 

1130.24 

1182.28 

1234.51 

1286.94 

1339.55 

19 

20 

924.63 

976.01 

1027.56 

1079.27 

1131.10 

1183.16 

1235.39 

1-287.81 

1340.43 

20 

•21 

925.48 

976.86 

1028.42 

1080.13 

1131.97 

1184.02 

1236.26 

1-288.69 

1341.30 

21 

22 

926.34 

977.72 

1029.27 

1080.99 

1132.83 

1184.88 

1237.13 

1289.57 

1342.18 

22 

23 

927.19 

978.58 

1030.13 

1081.86 

1133.70 

1185.75 

1238.00 

1290.44 

1343.06 

23 

24 

928.05 

979.44 

1080.99 

1082.72 

1134.56 

1186.62 

1238.87 

1291.32 

1343.94 

24 

25 

928.90 

980.29 

1031.85 

1083.58 

1135.43 

1187.49 

1239.74 

1-292.20 

1344.81 

25 

26 

929.76 

981.15 

1032.71 

1084.45 

1136.29 

1188.36 

1-240.61 

1293.07 

1345.69 

26 

27 

930.61 

982.01 

1033.57 

1085.31 

1137.16 

1189.23 

1-241.49 

1293.95 

134657 

27 

28 

931.47 

982.86 

1034.43 

1086.17 

1138.02 

1190.10 

1242.36 

1294.83 

1347.44 

28 

29 

932.32 

983.72 

1035.29 

1087.04 

1138.89 

1190.97 

1243.23 

1295.70 

1348.32 

29 

30 

933.18 

984.58 

1036.15 

1087.90 

1139.75 

1191.84 

1-244.10 

1-296.58 

1349.20 

30 

31 

934.04 

985.44 

1037.01 

1088.76 

1140.62 

1192.71 

1244.97 

1297.46 

135i).08 

31 

32 

934.89 

986.30 

1037.87 

1089.63 

1141.48 

1193.58 

1245.85 

1-298.33 

1350.96 

32 

33 

935.75 

987.16 

1038.74 

1090.49 

1142..35 

1194.45 

1246.72 

1-299.21 

1351.85 

33 

34 

936.60 

988.02 

1039.60 

1091.35 

1143.22 

1195.32 

1247.59 

1300.09 

13.52.73 

34 

33 

937.46 

988.88 

1040.46 

1092.22 

1144.09 

1196.19 

1248.46 

1300.96 

1353.61 

35 

36 

938.32 

989.74 

1041.32 

1093.08 

1144.95 

1197.06 

1-249.34 

1301.84 

1354.49 

36 

37 

939.17 

990.60 

1042.18 

1093.94 

1145.82 

1197.93 

1250.21 

1302.72 

1355.37 

37 

38 

940.03 

991.46 

1043.05 

1094.81 

1146.69 

1198.80 

1-251.08 

1303.59 

1356.25 

38 

39 

940.88 

992.32 

1043.91 

1095.67 

1147.55 

1199.68 

1251.95 

1304.47 

1357.14 

39 

40 

941.74 

993.18 

1044.77 

1096.53 

1148.42 

1200.55 

1252.83 

1305.35 

1358.02 

40 

41 

942.60 

994.04 

1045.63 

1097.40 

1149.29 

1201.42 

1253.70 

1306.-22 

1358.90 

41 

42 

913.45 

994.90 

1046.49 

1098.26 

1150.15 

1202.29 

1254.57 

1307.10 

1359.78 

42 

43 

914.31 

995.76 

1047.36 

1099.12 

1151.02 

1203.16 

1255.44 

1307.98 

1360.66 

43 

44 

945.16 

996.62 

1048.22 

1099.99 

1151.89 

1204.03 

1-256.32 

1308.85 

1361.54 

44 

45 

946.02 

997.48 

1049.08 

1100.85 

1152.76 

1204.90 

1257.19 

1309.73 

1362.43 

45 

46 

946.88 

998.34 

1049.94 

1101.71 

1153.62 

1205.77 

1-258.06 

1310.61 

1363.31 

46 

47 

947.73 

999.19 

1050.80 

1102.58 

1154.49 

1206.64 

1258.93 

1311.48 

1364.19 

47 

48 

948.59 

1000.95 

1051.67 

1103.44 

1155.36 

1207.51 

1259.81 

131-2.36 

1365  07 

48 

49 

919.44 

1000.91 

1052..53 

1104.30 

1156.'22 

1208.38 

1260.68 

1313.24 

1365.95 

49 

50 

950.30 

1001.77 

1053.39 

1105.17 

1157.09 

1209.25 

1-261.55 

1314.11 

1366.83 

50 

51 

951.16 

1002.63 

1054.25 

1106.03 

1157.96 

1210.12 

1262.42 

1314.99 

1367.72 

51 

52 

952.01 

1003.49 

1055.11 

1106.89 

1158.82 

1210.99 

1263.30 

1315.87 

1368.60 

52 

53 

952.87 

1004.35 

1055.98 

1107.76 

1159.69 

1211.86 

1-264.17 

1316.74 

1369.48 

53 

54 

953.72 

1005.21 

1056.84 

1108.62 

1160.56 

1212.73 

1265.04 

1317.62 

1370.36 

54 

55 

954.58 

1006.07 

1057.70 

1109.48 

1161.43 

1213.61 

1265.92 

1318.50 

1371.24 

65 

56 

955.44 

1006.93 

1058.56 

1110.35 

1162.29 

1214.48 

1266.79 

1319.37 

1372.12 

56 

57 

956.29 

1007.79 

1059.42 

1111.21 

1163.16 

1215.35 

1267.66 

1320.25 

1373.01 

67 

58 

957.15 

1008.65 

1060.28 

1112.07 

1164.03 

1216.22 

1268.53 

13-21.13 

1373.89 

58 

59 

958.00 

1009.51 

1061.14 

1112.94 

1164.89 

1217.09 

1269.41 

1322.00 

1374.77 

59 

21 


RAILROAD  CURVE  TABLES. 

t 

0 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35^ 

f 
0 

1375.65 

1428.65 

1481.89 

1635.30 

1589.04 

1643.08 

1697.28 

1751.83 

1.800.67 

1 

1376.53 

1429.54 

1482.78 

1536.20 

1589.94 

1643.98 

1698,19 

1752.74 

1807.59 

1 

2 

1377.41 

14:i0.42 

1483.67 

1537,09 

1590.84 

1644.88 

1699.10 

17.53,66 

1808,50 

2 

3  1378.30 

1431.31 

1484.56 

1537.99 

1591.74 

1646.78 

1700.01 

1754.67 

1809.42 

3 

4  :137y.l8 

1432.20 

1485.45 

1.538.88 

1.592.64 

1646.69 

1700,92 

1755,18 

1810.34 

4 

6  i;f80.06 

1433.08 

1486.34 

1539.78 

1.593.54 

1647.59 

1701.83 

1756.40 

1811.26 

6 

6  1380.91 

1433.97 

1487.23 

1540.67 

1594.44 

1648.49 

1702.74 

1757.31 

1812.17 

6 

7  1381.82 

1434.86 

1488.12 

1.541.57 

1.595.34 

1649,39 

1703.65 

1758.22 

1813.09 

7 

8  il38-.>.70 

1435.74 

1489.01 

1542.47 

1.596.24 

1650.29 

1704.55 

1759.13 

1814,00 

8 

9  1383..59 

1436.6! 

1489.90 

1543.36 

1597.14 

1651.19 

1705.46 

1760.05 

1814.92 

9 

10  1384.47 

1437,52 

1490.79 

1544.26 

1.598.04 

16.52.09 

1706.37 

1760.96 

1815.84 

10 

11  1385.3.5 

I4;i8.40 

1491.08 

1515.15 

1598.94 

1052.99 

1707,28 

1761.87 

1816.75 

11 

12  il3S6.23 

1439.29 

1492.57 

1546,05 

1599.84 

1653.90 

1708.19 

1762  79 

1817.07 

12 

13  li;i87.H 

14J0.18 

1493.46 

1540,94 

1000.74 

16.54.80 

1709.10 

1763.70 

1818,,59 

13 

14  {1387.99 

1441.06 

1494.35 

1547.84 

1601.64 

l(i55.70 

1710.01 

1764.61 

1819,50 

14 

15  '1388.88 

1441.95 

1495.24 

1548.74 

1002.54 

1656.60 

1710.92 

1765.53 

18i0.42 

15 

16 

1389.76 

1412.84 

1496.13 

1549.03 

1603.44 

1657.50 

1711.83 

1766.44 

1821  34 

16 

17 

1390.04 

1443.72 

1497.02 

1550.53 

1604,33 

1058.40 

1712,74 

1767.35 

1822,25 

17 

18 

1391.52 

1444.01 

1497.91 

1551.42 

1605.23 

1659.30 

1713.65 

1768.26 

1823.17 

18 

19 

1392.40 

1445  50 

1498.80 

1552,32 

1606.13 

1660.20 

1714.56 

1769.18 

1824.09 

19 

20 

1393.28 

144ii.38 

1499.69 

1553.21 

1607.03 

1061  11 

1715.47 

1770.<i9 

1825,00 

20 

21 

1394.17 

1447.27 

1500.58 

1.554.11 

1007.93 

16()2.01 

1716.38 

1771.00 

1825.92 

21 

22 

1395.05 

1448.16 

1501.47 

1555.00 

1608.83 

1662.91 

1717.28 

1771.92 

1826.84 

22 

23 

1395.93 

1449.04 

1502.36 

1555.90 

1609.73 

1663.81 

1718,19 

1772.83 

1827.75 

23 ; 

24 

1396.81 

1449.93 

1503.25 

1556,80 

1610.63 

1664.71 

1719.10 

1773.74 

1828.67 

24! 

25 

1397.69 

1450,82 

1504.14 

1557.69 

1611.53 

1605.61 

1720.01 

1774.66 

1829,59 

25 

26 

1398.57 

1451.70 

]  505,03 

1558.59 

1612.43 

1666.51 

1720.92 

1775.57 

1830.60 

26 

27 

1399.46 

1452.59 

1505.92 

15.59.48 

1613.33 

1667.42 

1721.83 

1776.48 

1831.42 

27 

28 

1400.34 

14.53.48 

1506.81 

1560.38 

1614.23 

1668.32 

1722.74 

1777..39 

18.32.34 

28 

29 

1401.22 

1454  36 

1507.70 

1561.28 

1015,13 

1669.22 

1723.65 

1778.31 

1833.'z5 

29 

30 

14(12.10 

1453.25 

1508.59 

1E62.17 

1616.03 

1670.12 

1724.56 

1779.22 

1834.17 

30 

31 

1402.99 

1456.U 

1509.48 

1563.07 

1610.93 

1671.03 

1725.47 

1780.14 

1835.09 

31 

32 

1403.87 

1457.03 

1510.37 

15(13.1)6 

1617.83 

1671.93 

1726.38 

1781.05 

1836.01 

32 

33 

1401.7(3 

U57.91 

1511.26 

1564.86 

1618.74 

1672.84 

1727.29 

1781.97 

1830.93 

33 

34 

1405.64 

1458.80 

1512.15 

1565.75 

1619.64 

1673.74 

1728.20 

1782.88 

1837.85 

34 

35 

140(;.53 

1459.69 

1513.04 

1566.65  i  1020.54 

1674.65 

1729.10 

1783.80 

1838.77 

35 

36 

1407.41 

1460.58 

1513,93 

1.567.54 

1021.44 

1675..55 

1730.01 

1784.71 

1839,69 

36 

37 

1-108.3O 

1461.47 

1514.82 

1568.44 

1(522.34 

1076.46 

1730.92 

1785.03 

1810.61 

37 

38 

I40.M8 

1462.35 

1515.71 

1569.34 

1023.24 

1677,30 

1731.83 

1786.54 

1841.54 

38 

39 

1410.07 

1403.24 

1516.60 

1.570.23 

1624.15 

1678.27 

1732.74 

1787.46 

1842.46 

39 

40 

1410.95 

1464.13 

1517.49 

1571.13 

1025.05 

1079.17 

1733.05 

17H8.37 

1843.38 

40 

41 

1411.84 

1405.02 

1518.38 

1572.02 

1625.95 

1080,08 

1734.,'JO 

1789.29 

1844,30 

41 

42 

1412.72 

1465.91 

1519.27 

1572.92 

1626.85 

1680.98 

1735.47 

1790.20 

1845.22 

42 

43 

1413.61 

1406.79 

1520.16 

1573.81 

1627.75 

1681.89 

.1736.38 

1791.12 

1816.14 

43 

44 

1414.49 

1407.68 

1521.05 

1.574.71 

1628.05 

1082.79 

1737.29 

1792.03 

1847.06 

44 

45 

1415.38 

1468.57 

1521.94 

1575.61 

1029.50 

1683,70 

1738.20 

1792.95 

1847,98 

46 

46 

1416.26 

1469.46  j 

1522.83 

1.576.50 

1630.46 

1()84.61 

17.39.10 

1793.80 

1848,90 

46 

47 

1417.15 

1470.35 

1523.73 

1577.40 

1631.36 

1685,51 

1740.01 

1794.78 

1819.82 

47 

48 

1418.03 

1471.23 

1524.62 

1578.29 

1632.26 

1686.42 

1740.92 

1795.69 

1850.74 

48 

49 

1418.92 

1472.12 

1525.51 

1.579.19 

1033.16 

1687..32 

1741.83 

1796.61 

1851.00 

49 

50 

1419.80 

U73.01 

1520.40 

1580.08 

1(;34.06 

1688.23 

1742,74 

1797.52 

18.52.58 

50 

51 

1420.69 

1473.90 

1527.29 

1580.98 

1034.97 

1689.13 

1743.65 

1798.44 

18.53  50 

51 

52 

1421.57 

1474.79 

1528.18 

1581.88 

1635.S7 

1690.04 

1744.56 

1799.35 

1854.43 

52 

63 

1422.46 

1475.67 

1529.07 

1582.77 

1036,77 

1690.94 

1745.47 

1800.27 

1855.35 

53  - 

54 

1423.34 

1470.56 

1529.96 

1583.67 

10.37.67 

1091.85 

1746.38 

1801.18 

1856.27 

54 

65 

1424.23 

1477.45 

1530.85  1 

1584.56 

1638.57 

1692.75 

1747,29 

1802.10 

1857.19 

55 

56 

1425.11 

1478.34 

.531.74 

1585.46 

16.39.47 

1693.66 

1748.19 

1803.01 

1858,11 

66 

57 

1425  99 

1479.23 

1532.63 

15S6.35 

1610.38 

1694.56 

1719.10 

1803.93 

1859.03 

57 

58 

1426  88 

1480.11 

533.52  , 

1587.25 

1641.28 

1695,47 

17.50.01 

1804.84 

1859.95 

58 

59 

1427.77  1481. no 

1.534.41  1.58,'<.15  !  1642  18  '  1096.37  '  17.-)n.92  i  1805,76  '  1860.87 

59 

22 


RAILROAD  CURVE  TABLES. 

'  1  36°  1  37°  j  38^  1  39°  |  40°  |  41^  |  42^  |  43°  |  44°  |  ' 

0  1861.79 

1917.26 

1973.01 

2029.11  2085.55  2142.33  ,  2199.52  2257.10 

2315.09 

0 

1 

1862.71 

1918.19 

1973.94 

2030.05 

2086,50 

2143,28 

2200.48 

2258.06 

2316.06 

1 

2 

1863.64 

1919.11 

1974.88 

2030.99 

2087.44 

2144.24 

2201.44 

2-25U.03 

2317.03 

2 

3 

1864.56 

1920.04 

1975.81 

2031.93 

2088.39 

2145.19 

2202.40 

2259.99 

2318.00 

3 

4 

1865.48 

1920.97 

1976.75 

2032.87 

2089.;J3 

2146.14 

2203.35 

2260.96 

2318.97 

4 

5 

1866.41 

1921.89 

1977.68 

20a3.81 

2090.28 

2147.10 

2204.31 

2261.92 

2319.94 

5 

6 

1867.33 

1922.82 

1978.61 

2034.75 

2091.22 

2148.05 

2205.27 

2262.89 

2320.91 

6 

7 

1868.25 

1923.74 

1979.55 

2035.69 

2092.17 

2149,00 

2206.23 

2263.85 

2321.88 

7 

8 

1869.17 

1924.67 

1980.48 

2036.63 

2093.11 

2149.95 

2207.19 

2264.82 

2322.85 

8 

9 

1870.10 

1925.60 

1981.42 

2037.67 

2094,06 

2150.91 

2208.15 

2265.78 

2323.82 

9 

10 

1871.02 

1926.52 

1982.35 

2038.51 

2095.00 

2151.86 

2209.11 

2266.75 

2324.79 

10 

11 

1871.94 

1927.45 

1983.28 

2039.45 

2095.95 

2152.81 

2210.07 

2267.71 

2325.76 

11 

,  12 

1872.86 

1928.38 

1984.22 

2040.39 

2096.89 

2153,77 

2211.02 

2268.68 

2326.73 

12 

13 

1873.78 

1929.30 

1985.15 

2041.33 

2097.84 

2154,72 

2211.98 

2269.64 

2327.70 

13 

14 

1874.71 

1930.23 

1986.09 

2042.27 

2098.78 

2155.67 

2212.94 

2270.61 

3328.67 

14 

15 

1875.63 

1931.15 

1987.02 

2043.21 

2099.73 

2156.63 

2213.90 

2271.57 

2329.64 

15 

16 

1876.55 

1932.08 

1987.95 

2044.15 

2100.67 

2157.58 

2214.86 

2272.54 

2330.61 

16 

17 

1877.48 

1933.01 

1988.89 

2045.08 

2101.62 

2158  53 

2215.82 

2273.50 

2331.59 

17 

18 

1878.40 

1933.93 

1989.82 

2046.02 

2102.57 

2159.48 

2216.78 

2274.46 

2332.56 

18 

19 

1879.32 

1934.86 

1990,76 

2046.96 

2103.51 

2160.44 

2217.74 

2275.43 

2333.52 

19 

20 

1880.24 

1935.79 

1991.69 

2047.90 

2104.46 

2161.39 

2218.69 

2276.39 

2334.49 

20 

21 

1881.16 

1936.71 

1992,62 

2048.84 

2105.40 

2162.34 

2219.65 

2277.36 

2335.46 

21 

22 

1882.09 

1937.64 

1993.56 

2049.78  ' 

2106.35 

2163.30 

2220.61 

2278.32 

2336.44 

22 

23 

1883.01 

1938.56 

1994.49 

2050,72 

2107.29 

2164.25 

2221.57 

2279.29 

2337.41 

23 

24 

1883.93 

1939.49 

1995.43 

2051.66 

2108.24 

2165.20 

2222.53 

2-280.25 

2338.38 

24 

25 

1884,86 

1940.42 

1996.36 

2052.60 

2109.18 

2166.16 

2223.49 

2281  22 

2339.35 

25 

26 

1885.78 

1941.34 

1997.29 

2053.54 

2110.13 

2167.11 

2224.45 

2-282.18 

2340.32 

26 

'27 

1886.71 

1942.27 

1998.23 

2054.48 

2111.07 

2168.06 

2225.40 

2-283.15 

2341.29 

•27 

28 

1887.63 

1943.20 

1999.16 

2055.42 

2112.02 

2169.01 

2226.36 

2-284.11 

2342.26 

28 

29 

1888.55 

1944.12 

2000.10 

2056.36 

2112.96 

2169.97 

2227.32 

2-285.08 

2343.23 

29 

30 

1889.47 

1945.05 

2001.03 

2057.30 

2113.91 

2170.92 

2228.28 

2286.04 

2344.20 

30 

31 

1890.40 

1945.98 

2001.97 

2058.24 

2114.86 

2171.87 

2229.24 

2-287.01 

2345.17 

31 

32 

1891.32 

1946.91 

2002.90 

2059.18 

2115.80 

2172.83 

2230.20 

2-287.98 

2346.15 

32 

33 

1892.25 

1947.85 

2003.84 

2060.13 

2116.75 

2173.78 

2231.16 

2288.94 

2347.12 

33 

34 

1893.17 

1948.78 

2004.77 

2061.07 

2117,70 

2174.73 

2232.12 

2-289.91 

2348.10 

34 

35 

1894.10 

1949.71 

2005.71 

2062.01 

2118.65 

2175  69 

2233  08 

2-290.88 

2349  07 

35 

36 

1895.03 

1950.64 

2006.65 

2062.95 

2119.59 

2176.64 

2234.04 

2291.85 

2350.04 

36 

37 

1895.95 

1951.57 

2007.58 

2063.89 

2120.54 

2177.59 

2235  00 

2292.82 

2351.02 

37 

38 

1896.88 

1952.51 

2008.52 

2064.83 

2121.49 

2178.55 

2235.97 

2-293.79 

2351.99 

38 

39 

1897.81 

1953.44 

2009.45 

2065.78 

2122.44 

2179.50 

2236.93 

2-294.75 

2352.'.i7 

39 

40 

1898.73 

1954.37 

2010.39 

2066.72 

2123.38 

21'-0.45 

2237.89 

2295.72 

2353.94 

40 

41 

1899.66 

1955.30 

2011.:W 

2067.66 

2124.33 

2181.41 

2238.85 

2-296.69 

2354.91 

41 

42 

1900.59 

1956.23 

2012.26 

2068.60 

2125.28 

2182.36 

2239.81 

2297.66 

2355.89 

42 

43 

1901.51 

1957.17 

2013.20 

2069.54 

2126,22 

2183.31 

2240  77 

2298.63 

2i56  86 

43 

|44 

1902.44 

1958.10 

2014.34 

2070.48 

2127.17 

2184.27 

2241.73 

2-299  60 

2357.84 

44 

1  45 

1903.36 

1959.03 

2015.07 

2071.43 

2128.12 

2185.22 

2242.69 

2.300  56 

2358.81 

45 

46 

1904.29 

1959.96 

2016.01 

2072.37 

2129.07 

2186.17 

2243.65 

2301.53 

2359.78 

46 

47 

1905.22 

1960.89 

2016.94 

2073.31 

2130.01 

2187.13 

2244  61 

230-2.5' » 

2360  76 

47 

48 

1906.14 

1961.a3 

2017.88 

2074.25 

2130.96 

•2188  08 

2245.57 

2303  47 

2361.73 

48 

49 

1907.07 

1962.76 

2018.81 

2075.19 

2131.91 

2189.03 

2246.53 

2.304.44 

2362.71 

49 

50 

1908.00 

1963.69 

2019.75 

2076.13 

213-2.86 

2189.99 

2247.49 

2305.41 

2363.68 

50 

51 

1908.92 

1964.62 

2020.69 

2077.08 

2133.80 

2190.94 

2248  45 

2306.37 

2364.65 

51 

52 

1909.85 

1965.55 

2021.62 

2078.02 

2134.75 

2191.89 

2249  42 

2307.34 

2.365  (;3 

62 

53 

1910.77 

1966.49 

2022.56 

2078.99 

2135.70 

2192.85 

2250.3S 

2308  31 

23  6  60 

53 

54 

1911.70 

1967.42 

2023.49 

2079.90 

2136.65 

2193  80 

2251.34 

23i)9.28 

2367.58 

54 

55 

1912.63 

1968.35 

2024.43 

2080.84 

2137.59 

2194.75 

2252.30 

2310.25 

2368.55 

55 

56 

1913.55 

1969.28 

2025.37 

2081.78 

2138.54 

2195.71 

2253.26 

2311.22 

2369.52 

56 

57 

1914.48 

1970.21 

2026.30 

2082.73 

2139,49 

2196  66 

2254.22 

2312.18 

2370.50 

57 

58 

1915.41 

1971.15 

2027.24 

2083.67 

2140.43 

2197.61 

2255.18 

2313.15 

2371.47 

5S 

59 

191G.33 

1972.08 

2028.17 

2084.61 

2141.38 

2198.57 

i  2256.14 

2314.21 

2372.45  .  59 

23 


RAILROAD  CURVE  TABLES. 

1 

45°  1  46°    47° 

1  48°  1  49°  1  50°  1  51° 

52°    53°  i  ' 

0 

2373.42 

2432.21 

2491.46 

2551.11 

2611.27 

2671.90  I  2733.04  i  2794.69 

2866.86 

0 

1 

2374.40 

2433.20 

2492.45 

2552.11 

2612.28 

2672.92 

2734.07 

1  2795.72 

2857.90 

1 

2 

23;5.:i8 

2434.18 

2493.45 

2553.11 

2613.29 

2673.94 

1  2735.09 

1  2796.76 

2858.95 

2 

3 

2376.35 

2435.17 

2494.44 

2554.11 

2614.30 

2674.95 

2736.12 

2797.79 

2859.99 

3 

4 

2377.33 

2436.15 

2495.43 

2555.11 

2616.31 

2675.97 

2737.14 

2798.82 

2861.03 

4 

6 

2378.31 

2437.14 

2496.43 

2550.11 

2616.32 

2676.99 

2738.17 

2799.86 

2862.08 

5 

6 

2379.29 

2438.12 

2497.42 

2567.12 

2617.32 

2678.01 

2739.19 

2800.89 

2863.12 

6 

7 

2380.27 

2439.11 

2498.41 

2558.12 

2618.33 

2679.03 

2740.22 

2801.92 

2864.16 

7 

8 

2381.24 

2440.10 

2469.40 

2559.12 

2619.34 

2680.04 

2741.25 

2802.96 

2865.20 

8 

9 

2382.22 

2441.08 

2500.40 

2560.12 

2620.35 

2681.06 

2742.27 

2803.99 

2866.26 

9 

10 

2383.20 

2442.07 

2501.39 

2561.12 

2621.36 

2682.08 

2743.30 

2806.02 

2867.29 

10 

11 

2384.18 

2443.05 

2502.38 

2662.12 

2622.36 

2683.10 

2744.32 

2806.06 

2868.33 

11 

12 

2385.16 

2444.04 

2503.38 

2563.12 

2623.37 

2684.12 

2745.35 

2807.09 

2869.38 

12 

13 

2386.13 

2445.02 

2504.37 

2564.12 

2624.3^ 

2686.13 

2746.37 

2808.12 

2870.42 

13 

14 

2387.11 

2446.01 

2505.36 

2565.12 

2625.39 

2686.15 

2747.40 

2809.16 

2871.46 

14 

15 

2388.09 

2447.00 

2506.36 

2566.12 

2626.40 

2687.17 

2748.43 

2810.19 

2872.51 

15 

16 

2389.07 

2447.98 

2507.35 

2567.13 

2627.41 

26H8.19 

2749.45 

2811.22 

2873.55 

16 

17 

2390.05 

2448.97 

2508.34 

2568.13 

2628.41 

2689.21 

2750.48 

2812.26 

2874.59 

17 

18 

2391.02 

2449.95 

2509.33 

2569.13 

2629.42 

2690.22 

2751.60 

2813.29 

2876.63 

18 

19 

2392.00 

2450.94 

2510.33 

2570.13 

2630.43 

2691.24 

2752.53 

2814.32 

2876.68 

19 

20 

2392.98 

2451.92 

2511.32 

2571.13 

2631.44 

2692.26 

2753.55 

2816.36 

2877.72 

20 

21 

2393.96 

2452.91 

2512.32 

2572.13 

2632.45 

2693.28 

2754.58 

2816.39 

2878.76 

21 

22 

2394.94 

2453.89 

2513.31 

2573.13 

2633.46 

2694.30 

2755.61 

2817.42 

2879.81 

22 

23 

2395.91 

2454.88 

2514.30 

2574.13 

2634.47 

2695.31 

2756.63 

2818.46 

2880.86 

23 

24 

2396.89 

2455.87 

2515.30 

2575.13 

26.35.48 

2696.33 

2757.66 

2819.49 

2881.89 

24 

25 

2397.87 

2456.85 

2516.29 

2576.13 

2636.49 

2697.35 

2758.08 

2820.52 

2882.94 

25 

26 

2398.85 

2457.84 

2517.28 

2577.13 

2637.50 

2698.37 

2769.71 

2821.56 

2883.98 

26 

27 

2399.83 

2458.82 

2518.27 

2578.13 

2638.50 

2699.39 

2760.73 

2822.59 

2885.02 

27 

28 

2400.80 

2459.S1 

2519.27 

2579.13 

2639.51 

2700.40 

2761.76 

2823.62 

2886.06 

28 

29 

2401.78 

2460.80 

2520.26 

2680.13 

2640.52 

2701.42 

2762.79 

2824.60 

2887.11 

29 

30 

2402.76 

2461.78 

2521.25 

2581.13 

2641.53 

2702.44 

2763.81 

2825.69 

2888.15 

30 

31 

2403.74 

2462.77 

2522.25 

2582,13 

2642.54 

2703.46 

2764.84 

2826.73 

2889.20 

31 

32 

2404.72 

2403.76 

2523.24 

2583.14 

2643.55 

2704.48 

2765.87 

2827.77 

2890.24 

32 

33 

2405.71 

2464.76 

2524.24 

2584.14 

2644.57 

2705.50 

2766.90 

2828.81 

2891.29 

33 

34 

2406.69 

2465.74 

2525.23 

2585.15 

2646.58 

2706.52 

2767.93 

2829.85 

2892.34 

34 

35 

2407.67 

2466.73 

2526.23 

2586.15 

2646.59 

2707.54 

2768.% 

2830.89 

2893.39 

35 

36 

2408.65 

2467.72 

2527.22 

2587.16 

2647.60 

2708.56 

2769.99 

2831.92 

2894.43 

36 

37 

2409.63 

2468.71 

2528.22 

2588.16 

2648.62 

2709.58 

2771.02 

2832.96 

2895.48 

37 

38 

2410.61 

2469.09 

2529.21 

2689.17 

2649.63 

2710.60 

2772.04 

2834.00 

2890.53 

38 

39 

2411.60 

2470.68 

2530-21 

2590.17 

2650.64 

2711.62 

2773.07 

2835.04 

2897.57 

39 

40 

2412.58 

2471.67 

2531.20 

2591.18 

2651.66 

2712.64 

2774.10 

2836.08 

2898.62 

40 

41 

•.i413.5(l 

2472.66 

2532.20 

2592.18 

2652.67 

2713.66 

2775.13 

2837.12 

2899.07 

41 

42 

2414.54 

2473.65 

2533.19 

2593.18 

2653.68 

2714.68 

2776.16 

2838.16 

2900.71 

42 

43 

2415.52 

2474.64 

2534.19 

2594.19 

2654.69 

2715.70 

2777.19 

2839.20 

2901.76 

43 

44 

2416.50 

2475.63 

2536.18 

2595.19 

2655.70 

2716.72 

2778.22 

2840.24 

2902.81 

44 

45 

2417.49 

2476.62 

2536.18 

2596.20 

2656.71 

2717.74 

2779.25 

2841.28 

2903.86 

46 

46 

2118.47 

2477.61 

2537.17 

2597.20 

2657.73 

2718.76 

2780.28 

2842.31 

2904.90 

46 

47 

2419.45 

2478.60 

2538.17 

2598.21 

2058.74 

2719.78 

2781.31 

2843.35 

2905.95 

47 

48 

'J420.43 

2479.59 

2539.17 

2599.21 

2659.75 

2720.80 

2782.34 

2844.39 

2907.00 

48 

49 

2421.4] 

2480.58 

2540.16 

260022 

2660.76 

2721.82 

2783.37 

2845.43 

2908.04 

49 

60 

2422.39 

2481.57 

2541.16 

2601.22 

2661.78 

2722.84 

2784.40 

2846.47 

2909.09 

60 

51 

2423.38 

2482.56 

2542.15 

2602.23 

2662.79 

2723.86 

2(85.43 

2847.51 

2910.14 

61 

52 

2424.36 

2483.54 

2543.15 

2603.23 

2003.80 

2724.88 

2786.45 

2848.55 

2911.18 

52 

53 

2425.34 

2484.53 

2544.14 

2604.24 

2664.81 

2725.90 

2787.48 

2849.59 

291223 

53 

54 

2426.32 

2485.52 

2545.14 

2605.24 

2665.83 

2726.92  1 

2788.51 

2850.63 

2913.28 

64 

55 

2427.30 

2480.51 

2546.13 

2606.24 

266!>.^4 

2727.94  ! 

2789.54 

2851.67 

2914.32 

55 

56 

2428.28 

2487.E0 

2547.13 

2607.25  1 

2667.85 

2728.95 

2790.57 

2852.70 

2915.36 

56 

57 

2429.27 

2488.49 

2548.12 

2608.25  1 

2668.K6 

2729.98 

2791.60  ! 

2853.74 

2916.41 

57 

58 

2430.25 

2489.48 

2549.12 

2609.26 

2669.87 

2731.00 

2792.63  : 

2854.78 

2917.46 

58 

69 

2431.23 

2490.47 

2650.11 

2610.26  , 

2670.89  2732.02 

2793.66  1 

2855.82  1  2918.50  1 

69 

24 


BAULBOAD  CURVK  TABLES. 

'  i  54-  I  55°  1  56°  }  57°  i  58°  |  59-  \   60°  |  61°  |  62^  |  ' 

0  1  2919.55  2982.81  ■■  3046.64  3111.10 

3176.14  1  3241.86  i 

3308.21 

3375.20 

3442.93 

0 

1 

29:0.60 

2983.87 

3047.71 

3112.18 

3177.23 

3242.96  1 

3309.32 

3370.33 

3444.07 

1 

2  1 

2921.65 

2984.93 

3048.78 

3113.26 

3178.32 

3244.06 

3310.44 

3377.45 

3445.20 

2 

a' 

2922.71 

2986.00 

3049.86 

3114.34 

3179.42 

3245.17 

3311.55 

3378.58 

3446.34 

3 

4 

2923.76 

2987.06 

3050.93 

3115.42 

3180.51 

3246.27 

3312.67 

3379.70 

3447.48 

4 

5i 

2^24.81 

2988.12 

3052.00 

3116.51 

3181.60 

3247.37 

3313.78 

3380.83 

3448.61 

5 

6 

2925.86 

2989.18 

3053.07 

3117.59 

3182.69 

3248.47 

3314.89 

3381.95 

3449.75 

6 

7 

29-26.92 

2990.24 

3054.14 

3118.67 

3183.79 

3249.57 

3316.01 

3383.08 

3450.88 

7 

8 

2927.97 

2991.31 

3055..;1 

3119.75 

3184.88 

3250.68 

3317.12 

3384.20 

3452.02 

8 

9 

2929.02 

2992.37 

3056.29 

3120.83 

3185.97 

3251.78 

3318.24 

3385.33 

3453.16 

9 

10 

2930.07 

2993.43 

3057.36 

3121.91 

3187.06 

3252.88 

3319.35 

3.386.45 

3454.29 

10 

11 

2931.13 

2994.49 

3068.43 

3122.99 

3188.16 

3i53.98 

3320.46 

3387.58 

3455.43 

11 

12 

2932.18 

2995.55 

3059.50 

3124.07 

3189.25 

3255.08 

3321.58 

3388.70 

3456.57 

12 

13 

2933.23 

2996.62 

3060.57 

3125.15 

3190.34 

3256.19 

3322.69 

3389.83 

3457.70 

13 

14 

2934.28 

2997.68 

3061.64 

3126.-23 

3191.43 

3257.29 

33-23.80 

3390.95 

3458.84 

14 

15 

2J35.33 

2998.74 

3062.72 

3127.32 

3192.52 

3258.39 

3324.92 

3392.08 

3459.97 

15 

16 

2'J3G.39 

2999.80 

3063.79 

3128.40 

3193.62 

3259.49 

3326.03 

3393.-20 

3461.11 

16 

17 

2937.44 

3000.86 

3064.86 

3129.48 

3194.71 

3260.59 

3327.15 

3394.33 

3462.25 

17 

18 

2'J38.49 

3001.93 

3065.93 

3130.56 

3195.80 

3261.70 

3328.26 

3395.45 

3463.38 

18 

19 

2»39.54 

3002.99 

3067.00 

3^31.64 

3196.89 

3262.80 

3329.36 

3396.58 

3464.52 

19 

20 

2940.60 

3004.05 

3068.07 

3132.72 

3197.99 

3263.90 

3330.49 

3397.70 

3465.66 

20 

21 

2941.65 

3005.11 

3069.15 

3133.80 

3199.08 

3265.00 

3331.60 

3398.83 

3466.79 

21 

22 

2942.70 

3006.17 

3070.22 

3134.S8 

3200.17 

3266.10 

3332.71 

3399.95 

3467.93 

22 

23 

2943.75 

3007.24 

3071.29 

3135.96 

3201.26 

3267.21 

3333.83 

3401.08 

3469.07 

23 

24 

2944.81 

3008.30 

3072.36 

3137.04 

3202.36 

3268.31 

3334.94 

3402.-20 

3470.20 

24 

25 

2^5.86 

3009.36 

3073.43 

3138.13 

3203.45 

3269.41 

3336.05 

3403.33 

3471.34 

25 

2U 

2946.91 

3010.42 

3074.50 

3139.21 

3204.54 

3270.51 

3337,17 

3404.45 

3472.47 

26 

27 

2947.96 

3011.48 

3075.58 

3140.29 

3205.63 

3271.61 

3338.28 

3405.58 

3473.61 

-27 

28 

2949.01 

3012.55 

3076.65 

3141.37 

3206.73 

3272.72 

3339.40 

3406.70 

3474.75 

28 

29 

2950.07 

3013.61 

3077.72 

3142.45 

3207.82 

3273.82 

3340.51 

3407.83 

3475.88 

29 

30 

2951.12 

3014.67 

307a.79 

3143.53 

3208.91 

3274.92 

3341.62 

3408.95 

3477.02 

30 

31 

2952.18 

3015.74 

3079.87 

3144.62 

3210.01 

3276.03 

3342.74 

3410.08 

3478.16 

31 

32 

2953.23 

3016.80 

3080.94 

3145.70 

3211.11 

3277.14 

3343.86 

3411.22 

3479.31 

32 

33 

2954.29 

3017.87 

3082.02 

3146.79 

3212.20 

3278.25 

3344.98 

341-2.35 

3480.45 

33 

34 

2955.35 

3018.93 

30-<3.10 

3147.88 

3213.30 

3279.36 

3346.10 

3113.48 

3481.60 

34 

35 

2956.40 

3020.00 

3084.18 

3148.97 

3214.40 

3280.47 

3347.22 

3414.61 

3482.74 

35 

36 

2957.46 

3021.06 

3085.25 

3150.05 

3215.50 

3-281.58 

3348.34 

3315.75 

3483.88 

36 

37 

2958.51 

t!022.13 

30H6.33 

3151.14 

3216.60 

3282.69 

3349.46 

3416.88 

3485.03 

37 

38 

2959.57 

3023.20 

3087.41 

3152.-3 

3217.70 

3283.80 

3350.58 

:i418.01 

3486.17 

38 

39 

2960.63 

3024.-.;6 

3088.48 

3153.31 

3218.80 

3-284.91 

3351.69 

3419.14 

3487.32 

39 

40 

2961.68 

3025.33 

3089.56 

3154.40 

3219.89 

3286.02 

3352.81 

3420.-28 

3488.46 

40 

41 

296-2.74 

3026.39 

3090.64 

3165.49 

3220.99 

3287.13 

3353.93 

3421.41 

3489.60 

41 

42 

2963.80 

3027.46 

3091.71 

3156.57 

3222.09 

3288.24 

3355.05 

3422.54 

3490.75 

42 

43 

2964.85 

3028.52 

3092.79 

3157.66 

3223.19 

3-289.35 

3356.17 

34-23.68 

3491.89 

43 

44 

2965.91 

3029.59 

3093.87 

3158.75 

3224,29 

3290.46 

3357.29 

34-24.81 

3493.04 

44 

45 

2966.96 

3030.66 

3094.95 

31.59.84 

3225.38 

3291.57 

3358.41 

3425.94 

3494.18 

45 

46 

2968.02 

3031.72 

3096.02 

3160.92 

3226.48 

3-292.68 

3359.53 

3427.07 

3495.32 

46 

47 

2969.08 

3032.79 

3097.10 

3162.01 

3227.58 

3293.78 

3360.65 

3428.21 

3496.47 

47 

48 

2970.13 

3033.85 

3098.18 

3163.10 

3228.68 

3-294.89 

3361.77 

3429.34 

3497.61 

48 

49 

2971.19 

3034.92 

3099.25 

3164.18 

3229.78 

3-296.00 

3362.89 

3430.47 

3498.77 

49 

50 

2972.25 

3035.98 

3100.33 

3165.27 

3230.88 

3297.11 

3364.01 

3431.60 

3499.90 

50 

61 

2973.30 

3037.05 

3101.41 

3166.36 

3231.97 

3298.22 

3365.13 

3432.74 

3501.04 

51 

52 

2974.36 

3038.11 

3102.48 

3167.44 

3233.07 

3299.33 

3366.25 

3433.87 

3502.19 

52 

53 

2975.41 

3039.18 

3103.56 

3168.53 

3234.17 

3300.44 

3367.37 

3435.00 

3503.33 

53 

51 

2976.47 

3040.25 

3104.64 

3169.62 

3235.27 

3301.55 

3368.48 

3436.13 

3r)04.48 

54 

55 

2977.53 

3041.31 

3105.72 

3170.71 

3236.37 

3302.66 

3369.60 

3437.27 

3505.62 

55 

66 

2978.58 

3042.38 

3106.79 

3171.79 

3237.47 

3303.77 

3370.72 

3438.40 

3506.76 

56 

57 

2979.64 

3043.44 

3107.87 

3172.88 

3238.56 

3304.88 

3371.84 

3439.53 

3507.91 

67 

58 

2980.70 

3044.51 

3108.95 

3173.97  i  3239.66 

3305.99 

3372.96 

3440.67 

3.509.05 

58 

69 

2981.75 

3045.57 

3110.02 

1  3175.05  [  3240.76 

3307.10 

3374.08 

3441.80 

3510.20 

,59 

25 


RAILROAD  CURVE  TABLES. 

'      63°    1    64° 

65°    1   660    j   67°       68° 

69° 

70°  1    71°    1   ' 

0 

3511.34 

3580.45    3650.41  1  3721.06 

3792.57 

3864.88 

3938.11 

4012.15 

4087.15 

0 

1 

8512.49 

3581.61 

3651.59 

3722.25 

3793.77 

3866.10 

3939.34 

4013.40 

4088.41 

1 

2 

3513.64 

3582.78 

3652.76 

3723.44 

3794.97 

3867.31 

3940.67 

4014.64 

4089.67 

2 

3 

3514.78 

3583.94 

3653,94 

3724.62 

37%.17 

3868.53 

3941.80 

4015.89 

4090.93 

3 

i 

3515.93 

3585.10 

3655.11 

3725.81 

3797.38 

3869.75 

3943.03 

4017.14 

4092.19 

4- 

6 

3517.08 

3586.27 

3656.29 

3727.00 

3798.58 

3870.97 

3944.26 

4018.39 

4093.45 

5 

6 

3518.23 

3587.43 

3657.46 

3728.19 

3799.78 

3872.18 

3945.49 

4019.63 

4094.71 

6 

7 

3519.38 

3588.59 

3658.64 

3729.38 

3800.98 

3873.40 

3946.72 

4020.88 

4095.97 

7 

8 

3520.52 

3589.75 

3659.81 

3730.56 

3802.18 

3874.62 

3947.95 

4022.13 

4097.24 

8 

9 

3521.67 

3590.92 

3660.99 

3731.75 

3803.38 

3875.83 

3949.18 

4023.37 

4098.50 

9 

0 

3522.82 

3592.08 

3662.16 

3732.94 

3804.58 

3877.05 

3950.41 

4024.62 

4099.76 

10 

1 

3523.97 

3593.24 

3663.33 

3734.13 

3805.78 

3878.27 

3951.64 

4025.87 

4101.02 

11 

2 

35J5.12 

3594.41 

3664.51 

3735.32 

3806.99 

3879.48 

3952.87 

4027.11 

4102.28 

12 

3 

3526.26 

3595.57 

3(;65.68 

3736.50 

3808.19 

3880.70 

3954.10 

4028.36 

4103.54 

13 

i 

3527.41 

3596.73 

3666.86 

3737.69 

3809.39 

3881.92 

3955.33 

4029.61 

4104.80 

14 

5 

3528.56 

3597.90 

3668.03 

3738.88 

3810.59 

3883.14 

3956.56 

4030.86 

4106.06 

15 

6 

3529.71 

3599.06 

3669.21 

3740.07 

3811.79 

3884.35 

3957.79 

4032.10 

4107.32 

16 

7 

35:10.86 

3600.22 

3670.38 

3741.26 

3812.99 

3885.57 

3959.02 

4033.35 

4108.58 

17 

8 

3532.00 

3(501.38 

3671.56 

3742.44 

3814.19 

3880.79 

3960.25 

4031.60 

4' 09.84 

18 

9 

35H3.15 

3602.55 

3672.73 

3743.63 

3815.39 

3888.00 

3961.48 

4035.84 

4111.10 

19 

0 

3534.30 

3603.71 

3673.90 

3744.82 

3816.60 

3889.21 

3962.71 

4037.09 

4112.36 

20 

1 

3535.45 

3604.87 

3675.08 

3746.01 

3817.80 

3890.43 

3963.94 

4038.34 

4113.62 

21 

2 

3536.60 

3606.04 

3676.25 

3747.20 

3819.00 

3891.64 

3965.17 

4039.58 

4114.89 

22 

3 

35;i7.74 

3607.20 

3677.43 

3748.38 

3820.20 

3892.86 

3966.40 

4040.83 

4116.15 

23 

i 

3538.89 

3608.36 

3678.60 

3749.57 

3821.40 

3894.08 

3967.63 

4042.08 

4117.41 

24 

5 

3540.04 

3609.53 

3679.78 

3750.76 

3822.60 

3895.29 

3968.86 

4043.33 

4118.67 

25 

6 

3541.19 

3610.69 

3680.96 

3751.95 

3823.80 

3896.51 

3970.09 

4044.57 

4119.93 

26 

7 

3542.34 

3611.85 

3682.13 

3753.14 

3825.01 

3897.73 

3971.32 

4045.82 

4121.19 

27 

18 

3543.48 

3613.01 

3683.30 

3754.32 

3826.21 

3898.95 

3972.55 

4047.07 

4122.45 

28 

9 

3544.63 

3614.18 

3684.48 

3755.51 

3827.41 

3900.16 

3973.78 

4048.31 

4123.71 

29 

to 

3545.78 

3615.34 

36H5.65 

3756.70 

3828.61 

3901.38 

3975.01 

4049.56 

4124.97 

30 

il 

3546.94 

3616.51 

36K6.83 

3757.90 

3829.82 

3902.60 

3976.25 

4050.81 

4126.24 

31 

!2 

3548.09 

3617.68 

3()88.01 

3759.09 

3831.03 

3903.83 

3977.49 

4052.07 

4127.51 

32 

J3 

3549.25 

3618.85 

3689.19 

3760.29 

3832.24 

3905,05 

3978.72- 

4053.32 

4128.78 

33 

J4 

3550.40 

3620.02 

3()90.37 

3761.48 

3833.45 

3906.28 

3979.96 

4054.57 

4130.06 

34 

J5 

3551.56 

3621.19 

3691.56 

3762.68 

3834.66 

3907.50 

3981.20 

405583 

4131.32 

35 

J6 

3552.72 

3622.35 

3692.73 

3763.87 

3835.86 

3908.73 

3982.44 

4057.08 

4132.59 

36 

n 

3563.87 

3623.52 

3693.91 

3765.07 

3837.07 

3909.95 

3983.68 

4058.33 

4133.86 

37 

}H 

3555.(3 

3624.69 

3695.09 

3766.27 

3838.28 

3911.17 

3984.91 

4059.58 

4135.13 

38 

39 

3556.18 

3625.86 

3696.27 

3767.46 

3839.49 

3912.40 

3986.15 

4060.84 

4136.40 

39 

10 

3557.34 

3627.03 

3697.45 

3768.66 

3840.70 

3913.62 

3987.39 

4062.09 

4137.67 

40 

41 

3558.49 

3628.20 

5698.63 

3769.85 

3841.91 

3914.85 

3988.63 

4063.34 

4138.94 

41 

12 

3559.65 

3629.37 

3699.81 

3771.05 

3843.12 

3916.07 

3989.87 

4064.60 

4140.21 

42 

13 

3560.80 

3630.54 

3700.99 

3772.24 

3844.33 

3917.30 

3991.10 

4065.85 

4141.48 

43 

14 

3561.96 

3631.71 

3702.17 

3773.44 

3845.54 

3918.52 

3992.34 

4067.10 

4142.75 

44 

45 

3563.12 

36:h2.88 

3703.35 

3774.64 

3846.75 

3919.74 

3993.58 

4068.36 

4144.02 

46 

46 

3564.27 

3631.04 

3704.53 

3775.83 

3847.95 

3920.97 

3994.82 

4069.61 

4145.29 

46 

47 

3565.43 

36.35.21 

3706.72 

3777.03 

3849.16 

3922.19 

3996.06 

4070.86 

4146.56 

47 

48 

3566.58 

3636.38 

3706.90 

3778.22 

3850.37 

3923.42 

3997.29 

4072.11 

4147.83 

48 

49 

3567.74 

3637.55 

3708.08 

3779.42 

3851.58 

3924.64 

3998.52 

4073.37 

4149.10 

49 

50 

3568.89 

3638.72 

3709.26 

3780.61 

3852.79 

3925.87 

3999.77 

4074.62 

4150.37 

50 

51 

3570.05 

3639.89 

3710.44 

3781.81 

3854.00 

3927.09 

4001.01 

4075.87 

4151.64 

61 

52 

3571.21 

3641.06 

3711.62 

3783.01 

3865.21 

3928.31 

4002.25 

4077.13 

4152.91 

52 

53 

3572.36 

3642.23 

3712.80 

3784.20 

3856.42 

3929.54 

4003  48 

4078.38 

4154.18 

63 

54 

3573.52 

3643.40 

3713.98 

3785.40 

3857.63 

3930.76 

4004.72 

4079.63 

4155.45 

54 

55 

3574.67 

3644.57 

3715.16 

3786.59 

3858.84 

3931.99 

4005.96 

4080.89 

4156.72 

65 

66 

3675.83 

3645.73 

3716.34 

3787.79 

3860.04 

3933.21 

4007.20 

4082.14 

4157.99 

66 

67 

3576.99 

3646.90 

3717.52 

3788.98 

3861.25 

3934.44 

4008.44 

4083.39 

1  4159.26 

57 

58 

3578.14 

3648.07 

3718.70 

3790.18 

3862.46 

3935.66 

4009.67 

4081  64 

4160.53 

58 

69 

3579.30 

3649.24 

3719.88 

3791.38 

3863.67  L  3936.88  1  4010.91 

4086.90 

,  4161.80 

69 

26 


RAILROAD  CURVE  TABLES. 

'  1  72°  1   73°  !  74°  1  75°  |  76°  |  77°  |  78°  |  79°  |  80°  |  ' 

0 

4163.07  4239.97 

4317.84 

4396.74 

4476.73 

4557.81 

4640.04 

4723.41 

4808.04 

0 

1 

4164.35 

4241.26 

4319.15 

4398.07 

4478.08 

4559.18 

4641.43 

4724.82 

4809.47 

1 

2 

4165.63 

4242.56 

4320.46 

4399.40 

4479.42 

4560.54 

4642.81 

4726.22 

4810.89 

2 

3 

4166.90 

4243.85 

4321.77 

4400.73 

4480.77 

4561.91 

4614.20 

4727.63 

4812.32 

3 

4 

4168.18 

4245.14 

4323.08 

4402.06 

4482.12 

4563.27 

4645.58 

4729.03 

4813.74 

4 

6 

4169.46 

4246.44 

4324.39 

4403.39 

4483.46 

4564.64 

4646.97 

4730.44 

4815,17 

5 

6 

4170.74 

4247.73 

4325.70 

4404.71 

4484.81 

4566.01 

4648.35 

4731.85 

4816.59 

6 

4172.02 

4249.02 

4327.01 

4406.04 

4486.16 

4567.37 

4649.74 

4733.25 

4818.02 

7 

8 

4173.29 

4250.31 

4328.32 

4407.37 

4487.51 

4668.74 

4651.12 

4734.66 

4819.44 

8 

9 

4174.57 

4251.61 

4329.63 

4408.70 

4488.85 

4570.10 

4652.50 

4736.06 

4820.87 

9 

10 

4175.85 

4252.90 

4330.94 

4410.03 

4490.20 

4571.47 

4653.89 

4737.47 

4822.29 

10 

11 

4177.13 

4254.19 

4332.25 

4411.36 

4491.55 

4572.83 

4655.27 

4738.87 

4823.72 

11 

12 

4178,41 

4255.49 

4333.56 

4412.69 

4492.89 

4574.20 

4656.66 

4740.28 

4825.14 

12 

13 

4179.68 

4256.78 

4334.87 

4414.02 

4494.24 

4575.56 

4658.04 

4741.68 

4826.57 

13 

14 

4180.96 

4258.07 

4336.18 

4415.35 

4495.59 

4576.93 

4659.43 

4743.09 

4827.99 

14 

15 

4182.24 

4259.36 

4337.49 

4416.68 

4496.93 

4578.30 

4660.81 

4744.50 

4829.42 

15 

16 

4183.62 

4260.66 

4338.80 

4418.01 

4498.28 

4579.66 

4662.20 

4745.90 

4830.84 

16 

17 

4184.80 

4261.95 

4340.11 

4419.34 

4499.63 

4581.03 

4663.58 

4747.31 

4832.27 

17 

18 

4186.07 

4263.24 

4341.42 

4420.67 

4500.98 

4582.39 

4664.97 

4748.71 

4833.69 

18 

19 

4187,35 

4264.54 

4342.73 

4422.00 

4502.32 

4583.76 

4666.35 

4750.12 

4835.12 

19 

20 

4188.63 

4265.83 

4344.05 

4423.33 

4503.67 

4585.12 

4667.73 

4751.52 

4836.54 

20 

•21 

4189.91 

4267.12 

4345.36 

4424.65 

4505.01 

4586.49 

4669.12 

4752.93 

4837.97 

21 

22 

4191.19 

4268.42 

4346.67 

4425.98 

4506.35 

4587.86 

4670.50 

4754.34 

4839.39 

22 

23 

4192.46 

4269.71 

4347.98 

4427.31 

4507.70 

4589.22 

4671.89 

4755.74 

4840.82 

23 

•U 

4193.74 

4271.00 

4349.29 

4428.64 

4509.05 

4590.59 

4673.27 

4757.15 

4842.24 

24 

25 

4195.02 

4272.29 

4350.60 

4429.97 

4510.39 

4591.95 

4674.66 

4768.55 

4843.67 

25 

26 

4196.30 

4273.59 

4351.91 

4431.30 

4511.74 

4593.32 

4676.04 

4759.% 

4846.09 

26 

27 

4197,57 

4274.  S8 

4353.22 

4432.63 

4513.09 

4594.69 

4677.43 

4761.37 

4846.52 

27 

28 

4198.85 

4276.17 

4354.53 

4433.96 

4514.44 

4596.05 

4678.81 

4762.77 

4847.94 

28 

29 

4200.13 

4277.47 

4355.84 

4435.29 

4515.78 

4597.42 

4680.20 

4764.18 

4849.37 

29 

30 

4201.41 

4278.76 

4357.15 

4436.62 

4517.13 

4598.78 

4681.58 

4765.68 

4850.79 

30 

31 

4202.70 

4280.06 

4358.47 

4437.96 

4518.49 

4600.15 

4682.97 

4766.99 

4862.23 

31 

32 

4203.98 

4281.36 

4359.79 

4439.29 

4519.84 

4601.53 

4684.37 

4768.41 

4853.66 

32 

33 

4205.27 

4282.67 

4361.11 

4440.63 

4521.20 

4602.91 

4685.76 

4769.83 

4855.10 

33 

34 

4206.55 

4283.97 

4362.43 

4441.97 

4522.55 

4604.28 

4687.16 

4771.24 

4866.53 

34 

35 

4207.84 

4285.27 

4363.75 

4443.30 

4523.91 

4605.66 

4688.55 

4772.66 

4857.97 

35 

36 

4209.12 

4286.58 

4365.07 

4444.64 

4525.27 

4607.03 

4689.94 

4774.07 

4859.41 

36 

37 

4210.41 

4287.88 

4366.39 

4445.98 

4526.62 

4608.41 

4691.34 

4775.49 

4860.84 

37 

38 

4211.69 

4289.18 

4367.71 

4447.32 

4527.98 

4609.78 

4692.73 

4776.90 

4862.28 

38 

39 

4212.98 

4290.48 

4369.03 

44*8.65 

4529.33 

4611.16 

4694.13 

4778.32 

4863.71 

39 

40 

4214.'26 

4291.79 

4370.35 

44*9.99 

4530.69 

4612.53 

4695.52 

4779.73 

4865.15 

40 

41 

4215.55 

4293.09 

4371.67 

4451.33 

4532.05 

4613.91 

4696.92 

4781.15 

4866.59 

41 

42 

4216.83 

4294.39 

4372.99 

4452.66 

4533.40 

4615.28 

4698.31 

4782.56 

4868.03 

42 

43 

4218.12 

429.5.69 

4374.31 

4454.00 

4534.76 

4616.66 

4699.70 

4783.98 

4169.46 

43 

44 

4219.40 

4297.00 

4375.63 

4455.34 

4536.11 

4618.03 

4701.10 

4785.39 

487ti.'.'0 

44 

45 

4220.69 

4298.30 

4376.94 

4456.67 

4537.47 

4619.41 

4702.49 

4786.81 

4872.33 

46 

46 

4221.98 

4299.60 

4378.26 

4458.01 

4538.83 

4620.78 

4703.89 

4788.22 

4873.77 

46 

47 

4223.26 

4300.91 

4379.58 

4459.35 

4540.18 

4622.16 

4705.28 

4789.64 

4875.21 

47 

48 

4224.55 

4302.21 

4380.90 

4460.69 

4541.54 

4623.53 

4706.67 

4791.05 

4876.61 

48 

49 

4225.83 

4303.51 

4382.22 

4462.02 

4542.89 

4624.91 

4708.07 

4792.47 

4878.0g 

49 

50 

4227.12 

4304.81 

4383.54 

4463.36 

4544.25 

4626.29 

4709.47 

4793.89 

487y.52 

60 

51 

4228.40 

4306.12 

4384.86 

4464.70 

4545.61 

4627.66 

4710  86 

4795.30 

4880.95 

61 

52 

4229.69 

4;}07.42 

4386.18 

4466.03 

4546.96 

46-29.04 

4712.25 

4796.72 

4882.39 

62 

53 

4230.97 

430H.72 

4387.50 

4467.37 

4548.32 

4630.41 

4713.65 

4798.13 

4883.83 

63 

64 

4232.26 

4310.02 

4388.82 

4468.71 

4549.67 

4631.79 

4715.04 

4799.55 

4885.26 

64 

65 

4233.54 

4311v33 

4390.14 

,  4470.04 

4551.03 

4633.16 

4716.44 

4800.96 

4886.70 

56 

56 

4234.83 

4312.63 

4391.46 

4471.38 

4552.39 

4634.54 

4717.83 

4802.38 

4888.13 

66 

57 

i  4236.11 

4313.93 

!  4392.78 

4472.72 

4553.74 

4635.91 

4719.22 

4803.79 

4889.57 

57 

58 

!  4237.40 

4315.23 

4.394.10 

4474.06 

4555.10 

'  4637.29 

4720.62 

4805.21 

4891.00 

58 

59 

4238.68 

,  4316.54  4395.42  4475.39 

,  4556.45 

4638.66 

4722.01 

4806.62 

4892.44 

59 

i 

27 


RAILROAD  CURVE  lABLES. 

'  j  81°  1  82^  1  83°  1  84°  |  85°  |  86^  |  87° 

88°  i  89°  1  ' 

0 

4893  88 

4980.97 

5069.44 

5159.29 

5250.57 

6343.28  1  5437.64 

5533.35 

5630.81 

0 

1 

4895.33 

4982.44 

5070.93 

6160.80 

5252.11 

5344.84 

5439.13 

6534.97 

5632.46 

1 

2 

4896.77 

4983  91 

6072.42 

5162.32 

6263.65 

6346.41 

6440.72 

5536  59 

6634.10 

2 

3 

4898.22 

4985.38 

6073.92 

5163.83 

5255.19 

6347.97 

6442.31 

5538,20 

6635.75 

3 

4 

4899,66 

4986.85 

6075.41 

5165.35 

5256.73 

5349.54 

5443.90 

6539.82 

5637.39 

4 

5 

4901.11 

4988.32 

6076.90 

5166.86 

5258.27 

5351.10 

6445.50 

5541.44 

5639.04 

6 

6 

4902.56 

4989.78 

5078.39 

6168.38 

6259.81 

6352.67 

5447.09 

5543.06 

5640.69 

6 

7 

4904.00 

4991.25 

5079.88 

6169.89 

6261.35 

5354.23 

5448,68 

5544.68 

564233 

7 

8 

4905.45 

4992.72 

6081  38 

5171.41 

5262.88 

5355.79 

5450.27 

6.546.29 

6643.98 

8 

9 

4906.89 

4994.19 

5082.87 

5172.92 

5264.42 

5357.36 

5451.86 

6547.91 

5645.63 

9 

10 

4908.34 

4995.66 

6084.36 

6174.44 

6265.96 

6358.92 

5453.45 

5549.53 

5647.27 

10 

11 

4909.78 

4997.13 

6085.85 

5175.95 

5267.50 

6360.49 

6455.04 

5551.14 

5648.92 

11 

12 

4911.23 

4998.60 

6087.34 

5177.47 

6269.04 

5362  05 

5456.63 

5552.76 

6650.57 

12 

13 

4912.68 

5000.07 

5088.84 

5178.98 

6270.58 

5363.62 

6458.22 

5554.38 

5652.21 

13 

14 

4914.12 

5001.54 

5090.33 

6180.50 

6272.12 

5365.18 

5459.81 

5556.00 

5653.86 

14 

15 

4915.57 

5003.01 

5091.82 

6182.01 

6273.66 

5366.74 

5461.41 

6657.62 

5655.60 

15 

16 

4917.01 

5004.47 

6093.31 

6183.53 

6275.20 

6368.31 

5463.00 

6559.24 

5657.15 

16 

17 

4918.46 

5005.94 

6094.80 

6185.04 

6276.74 

6369,87 

5464.59 

5560.85 

6658.80 

17 

18 

4919.91 

5007.41 

5096.30 

5186.56 

5278.28 

5371.44 

5466.18 

5562  47 

6660.44 

18 

19 

4921.35 

5008.88 

5097.79 

5188.07 

5279.82 

5373.00 

6467.77 

6564.09 

5662.09 

19 

20 

4922-79 

5010.35 

5099.23 

5189.58 

5281.36 

6374.57 

5469.36 

5565.70 

5663.74 

20 

21 

4924.24 

5011.82 

6100.77 

5191.10 

5282.90 

6376.13 

5470.95 

6567.32 

5665,38 

21 

22 

4925.69 

5013.29 

5102.26 

6192.61 

5284.44 

5377.69 

5472.54 

5568.94 

5667.03 

22 

23 

4927.13 

5014.76 

6103.76 

5194.13 

5286.97 

6379.26 

5474.13 

5570.56 

5668.67 

23 

24 

4928.58 

5016.23 

6105.25 

6195.64 

6287.51 

6380.82 

5475.72 

5572.18 

5670.32 

24 

25 

4930.02 

5017.69 

5106.74 

6197.16 

5289.05 

5382.39 

5477.32 

5573.79 

6671.97 

25 

26 

4931.47 

501916 

5108.23 

5198.67 

5290.59 

5383.95 

5478.91 

6575.41 

5673.61 

26 

27 

4932.92 

5020  63 

5109.72 

5200.19 

5292.13 

5385.51 

5480.50 

6577.03 

5675.26 

27 

28 

4934.36 

5022.10 

5111,22 

5201.70 

5293.67 

6387.08 

5482.09 

6578.65 

5676.91 

28 

29 

4935.81 

5023.57 

5112.71 

5203.22 

5295.21 

5388.64 

5483.68 

5580.27 

5678,55 

29 

30 

4937.25 

5025.04 

6114.20 

6204.73 

5296.75 

6390.21 

548$.27 

5581.88 

5680.20 

30 

31 

4938.71 

5026  52 

6115  70 

6206.26 

5298.30 

5391.79 

6486.87 

5583.51 

5681.86 

31 

32 

4940.16 

5028.00 

6117.21 

5207.79 

5299.85 

5393.37 

5488.48 

5585.14 

5683.62 

32 

33 

4941.62 

5029.48 

6118.71 

5209.31 

5301.40 

5394.94 

5490.08 

5586.77 

5685.18 

33 

34 

4943.08 

5030.96 

5120.21 

5210.84 

5302.95 

5396.52 

5491  68 

5588.40 

5686.84 

34 

35 

4944  54 

5032  44 

5121.72 

5212.37 

5304.51 

6398.10 

5493.29 

6590.04 

5688,50 

35 

36 

4945.99 

5033.92 

5123.22 

6213.90 

6306.06 

5399.68 

6494.89 

6591.67 

5690.16 

36 

37 

4947.45 

5035.40 

6124.72 

5215.43 

5307.61 

5401.25 

5496.49 

5593.30 

5691.82 

37 

38 

4948.91 

6036.88 

5126.22 

5216  95 

5309.16 

6402.83 

6498.09 

5594.93 

5693,48 

38 

39 

4950.36 

5038  36 

5127.73 

5218.48 

5310.71 

6404.41 

5499.70 

5596.56 

5695,14 

39 

40 

4951.82 

5039.84 

5129.23 

5220,01 

5312.26 

5405.99 

5501.30 

5598.19 

5696.80 

40 

41 

4953.28 

5041.32 

5130.73 

5221.54 

5313.81 

5407.56 

5502.90 

5599.82 

5698.46 

41 

42 

4954.74 

5042.80 

5132.24 

5223  07 

5315.36 

5409.14 

5504.60 

5601.45 

5700.12 

42 

43 

4956.19 

5044.28 

6133  74 

6224.59 

6316.91 

5410.72 

5506.11 

5603.08 

5701.78 

43 

44 

49.'i7.65 

5045.76 

5135.24 

5226.12 

5318.46 

5412.30 

5507.71 

5604.71 

5703.44 

44 

45 

49,59.11 

5047.24 

5136.75 

5227.65 

5320.02 

5413.88 

5509.31 

5606.35 

5705.10 

45 

46 

4960.57 

5048.72 

6138.26 

5229.18 

5321  57 

5416.45 

5510.91 

6607.98 

5706.76 

46 

47 

4962.02 

5050  20 

5139.75 

5230.71 

5323.12 

5417.03 

5512.52 

5609.61 

5708.42 

47 

48 

4963.48 

5051.68 

5141,25 

5232.23 

5324.67 

5418.61 

5514.12 

5611.24 

6710.08 

48 

49 

4964.94 

5053.16 

5142.76 

5233.76 

5326.22 

6420.19 

5515.72 

5612.87 

6711.74 

49 

60 

4966,40 

5054.64 

5144  26 

5235.29 

5327.77 

5421.76 

5517.32 

5614.50 

5713.40 

50 

51 

4967.85 

6056.12 

5145.76 

6236.82 

5329  32 

5423,34 

5518.93 

5616.13 

5715.06 

51 

52 

4979.31 

5057.60 

5147.27 

5238.35 

5330.87 

6424.92 

5520.53 

5617.76 

5716.72 

52 

53 

4970.77 

5059.08 

5148.77 

5239.87 

5332.42 

5426.50 

5522.13 

5619.39 

5718  38 

53 

.  54 

4972.22 

5060.56 

5150.27 

5241.40 

5333.97 

5428.07 

5523.74 

5621.02 

6720.04 

54 

55 

4973.68 

5062.04 

5151.77 

5242.93 

5335.53 

5429.65 

5525.34 

5622.66 

5721.70 

65 

56 

4975.14 

5063.52 

5153.28 

5244,46 

5537.08 

5431.23 

5526.94 

5624.29 

5723.36 

56 

57 

4976.60 

5065.00 

5154.78 

5245.99 

6338.63 

5432.81  5528.54 

5625.92 

5725.02 

57 

68 

4978.05 

5066.48 

5156.28 

5247.51 

5340.18 

5434  39  5530.15 

5627.55 

5726.68 

58 

69 

4979.51 

5067-96 

5157.79 

5249.04 

5341.73 

5135.96  5531.75 

5629.18 

5728.34 

59 

28 


Table  of  Minutes  with  Cob- 
UESPONDING  Decimals. 

_ . . 1 

1  Table  of  Seconds  with  Gorkrh- 
poNDiNO  Decimals. 

M. 

1   i>. 

M. 

1   D. 

1  s. 

1    D. 

1   S. 

1    D. 

1 

1 

o 

0.0166 

31 

o 

0.5167 

1 

■1 
0.0002778 

31 

o 
0.0086111 

2 

0.0333 

32 

0.5333 

2 

0.0005556 

32 

0.0088888 

3 

0.0500 

33 

0.5500 

3 

0.0008333 

33 

9.0091666 

4 

0.0667 

34 

0.5667 

4 

0.0011111 

34 

0.0094444 

5 

0.0833 

35 

0.5833 

5 

0.0013888 

35 

0.0097222 

6 

0.1000 

36 

0.6000 

6 

0.0016666 

36 

0.0100000 

7 

0.1167 

37 

0.6167 

7 

0.0019444 « 

37 

0.0102777 

8 

0.1333 

38 

0.6333 

8 

0.0022222 

38 

0.0105555 

9 

0.1500 

39 

0.6500 

9 

0.0025000 

39 

0.0108333 

10 

0.1667 

40 

0.6667 

10 

0.0027777 

40 

0.0111111 

11 

0.1833 

41 

0.6833 

11 

0.0030555 

41 

0.0113888 

12 

0.2000 

42 

0.7000 

12 

0.0033333 

42 

0.0116666 

13 

0.2167 

43 

0.7167' 

13 

0.0036111 

43 

0.0119444 

14 

0.2333 

44 

0.7333 

14 

0.0038888 

44 

0.0122222 

15 

0.2500 

45 

0.7500 

15 

0.0041666 

45 

0.0125000 

16 

0.2667 

46 

0.7667 

16 

0.0044444 

46 

0.0127777 

17 

0.2833 

47 

0.7833 

17 

0.0047722 

47 

0.0130555 

18 

0.3000 

48 

0.8000 

18 

0.0050000 

48 

0.0133333 

19 

0.3167 

49 

0.8167 

19 

0.0052777 

49 

0.0136111 

20 

0.3333 

50 

0.8333 

20 

0.0055555 

50 

0.0138888 

21 

0.3500 

51 

0.8500 

21 

0.0058333 

51 

0.0141666 

22 

0.3667 

52 

0.8667 

22 

0.0061111 

52 

0.0144444 

23 

0.3833 

53 

0.8833 

23 

0.0063888 

53 

0.0147222 

24 

0.4000 

54 

0.9000 

24 

0.0066666 

54 

0.0150000 

25 

0.4167 

55 

0.9167 

25 

0.0069444 

55 

0.0152777 

26 

0.4333 

56 

0.9333 

26 

0.0072222 

56 

0.0155555 

27 

0.4500 

57 

0.9500 

27 

0.0075000 

57 

0.0158333 

28 

0.4667 

58 

0.9667 

28  i 

0.0077777 

58 

0.0161111 

29 

0.4833 

59 

0.9833 

29 

0.0080555 

59 

0.0163888 

30 

0.5000 

60 

1.0000 

30  1 

0.0083333 

60 

0.0166666 

RAILROAD  CURVE  TABLE. 


The  following  table  shows  the  distance  from  the  point  of  intersection 
of  the  tangent  lines  to  the  beginning  of  one  degree  curves,  for  each  30 
minutes,  the  angle  of  deflection  (=  angle  at  centre)  being  known. 
I.  =  The  given  angle  of  deflection. 
II.  =  The  sought  for  distance. 
III.  =  Difference  for  intermediate  angles. 
[This  table  is  an  abridgement  of  the  preceding  one,  and  is  to  be  used 
for  approximate  work  in  running  trial  curves.    When  the  curve  is  sharper 
than  five  degrees  it  will  be  well,  in  order  to  secure  good  results,  to  com- 
pute T  by  one  of  the  formulas  given  on  page  17.     In  using  both  tables  it 
should  be  borne  in  mind  that  the  100-foot  chain  can  alone  be  used,  and 
that  the  degree  of  curve  is  the  angle  subtended  at  the  center  by  a  chord 
100  feet  long.— The  Editor.] 


30 


RAILROAD 

CURVE 

TABLE. 

1    ^   1 

II 

III 

I     1 

II    1 

Ill    1 

I     1 

II   1 

III 

0°    o' 

25.00 

25.0 

30^ 

30 

1562.17 

26.8 

60^ 

30' 

3341.62 

33.4 

1 

50.02. 

25.0 

31 

1589.04 

26.9 

61 

3375.20 

33.6 

1    30 

75.01 

25.0 

31 

30 

1616.03 

27.0 

61 

30 

3408.95 

33.8 

2 

99.99 

25.0 

32 

1643.08 

27.0 

62 

3442.93 

34.0 

2    30 

125.03 

25.0 

32 

30 

1670.12 

27.0 

62 

30 

3477.02 

34.1 

3 

150.07 

25.0 

33 

1697.28 

27.2 

6.i 

3511.34 

34.3 

3    30 

175.05 

25.0 

33 

30 

1724.56 

27.3 

63 

30 

3545.78 

34.4 

4 

200.09 

25.0 

34 

1751.83 

27.3 

64 

3580.45 

34.7 

1    30 

225.13 

•25.0 

34 

30 

1779.22 

27.4 

64 

30 

3615.34 

34.9 

5 

250.17 

25.0 

35 

1806.67 

27.4 

65 

3650.41 

35.1 

5    30 

275.21 

25.0 

35 

30 

1834.17 

27.5 

65 

30 

3685.65 

35.2 

6 

300.30 

25.0 

36 

1861.79 

27.6 

66 

3721.06 

35.4 

6    30 

325.35 

25.0 

36 

30 

1889.47 

27.7 

66 

30 

3756.70 

356 

7 

350.44 

25.1 

37 

1917.26 

27.8 

67 

3792.57 

35.9 

7    30 

375.54 

25.1 

37 

30 

1945.05 

27.8 

67 

30 

3828.61 

36.0 

8 

400.70 

25.1 

38 

1973.01 

27.9 

68 

3864.88 

36.3 

8    30 

426.79 

25.1 

38 

30 

2001.03 

28.0 

68 

30 

3901.38 

36.5 

9 

450.95 

25.1 

39 

2029.11 

28.1 

69 

3938.11 

36.7 

9    30 

476.10 

25.1 

39 

30 

2057.30 

28.2 

69 

30 

3975.01 

36.9 

10 

501.32 

25.2 

40 

2085.55 

28.3 

70 

4012.15 

37.1 

10    30 

526.53 

25.2 

40 

30 

2113.91 

2m.  4 

70 

30 

4019.56 

37.4 

i    11 

551.74 

25.2 

41 

2142.33 

28.4 

71 

4087.15 

37.6 

11    30 

576.95 

25.2 

41 

30 

2170.92 

28.6 

71 

30 

4124.97 

37.8 

12 

602.22 

25.3 

42 

2199.52 

28.6 

72 

4163.07 

38.1 

1-2    30 

627.55 

25.3 

42 

30 

2228.28 

28.8 

72 

30 

4201.41 

38.3 

13 

652.87 

25.3 

43 

2257.10 

28.8 

73 

4239.97 

38.6 

13    30 

678.20 

25.3 

43 

30 

2286.04 

28.9 

73 

30 

4278  76 

38.8 

14 

703.53 

25.3 

44 

2315.09 

29.0 

74 

4317.84 

38.9 

11    30 

728.97 

25.4 

44 

30 

2344.20 

29.1 

74 

30 

4357.15 

39  3 

15 

754.35 

25.4 

45 

2373.42 

29.2 

75 

4396.74 

39.6 

15    30 

779.79 

25.4 

45 

30 

2402.76 

29.3 

75 

30 

4436.62 

39.9 

16 

805.29 

25.5 

46 

2432.21 

29.4 

76 

4476.73 

40.1 

16    30 

830.79 

25.5 

46 

30 

2461.78 

29.6 

76 

30 

4517.13 

40.4 

17 

856.35 

25.5 

47 

2491.46 

29.7 

77 

4557.81 

40.7 

17    30 

881.90 

25.5 

47 

30 

2521.26 

29.8 

77 

30 

4598.78 

41.0 

18 

907.52 

25.6 

48 

2551.11 

29.8 

78 

4640.04 

41.3 

18    30 

933.18 

25.6 

48 

30 

2581.13 

30.0 

78 

30 

4681.58 

415 

19 

958.86 

25.7 

49 

2611.27 

30.1 

79 

4723.41 

41.8 

19    30 

984.58 

25.7 

49 

30 

2641.53 

30.3 

79 

30 

4765.58 

42.2 

20 

1010.37 

25.8 

50 

2671.90 

30.4 

80 

4808.04 

42.5 

20    30 

1036.15 

25.8 

50 

30 

2702.44 

30.5 

80 

30 

4850.79 

42.7 

21 

1062.00 

25.8 

51 

2733.04 

30.6 

81 

4893.88 

43.1 

21     30 

1089.90 

25.9 

51 

30 

2763.81 

30.8 

81 

30 

4937.25 

43.3 

22 

1113.80 

25.9 

52 

2794.69 

30.9 

82 

4980.97 

43.7 

22    30 

1139.75 

25.9 

52 

30 

2825.M 

31.0 

82 

30 

5025.04 

44.1 

23 

1165.76 

26.0 

53 

2856.86 

31.2 

83 

6069.44 

44.4 

23    30 

1191.84 

26.1 

53 

30 

2888.15 

31.3 

83 

30 

5114.20 

44.8 

24 

1217.96 

26.1 

54 

2919.55 

31.4 

84 

5159.29 

45.1 

24    30 

1244.10 

26.1 

54 

30 

2951.12 

31.6 

84 

30 

5204.73 

45.4 

25 

1270.28 

26.2 

55 

2982.81 

31.7 

85 

5250.57 

45.8 

25    30 

1296  58 

26.3 

55 

30 

3014.67 

31.9 

85 

30 

5296.75 

46.2 

26 

1322.88 

26.3 

56 

3046.64 

32.0 

86 

5343.28 

46.5 

26    30 

1349.24 

26.4 

56 

30 

3078.79 

32.2 

86 

30 

5330.21 

46.9 

27 

1375.65 

26.4 

57 

3111.10 

32.3 

87 

5437.54 

47.3 

27    30 

1402.10 

26.4 

57 

30 

3143.53 

32.4 

87 

30 

5485.27 

47.7 

28 

1428.65 

26.5 

58 

3176.14 

32.6 

88 

5533.35 

48.1 

28    30 

1455.25 

26.6 

58 

30 

3208.91 

32.8 

88 

30 

5581.88 

48.5 

29 

1481.89 

266 

59 

3241.86 

32.9 

89 

5630.81 

48.9 

29    30 

1508.59 

26.7 

59 

30 

3274.92 

33.1 

89 

30 

5680.20 

49.4 

30 

1535.30 

26.7 

60 

3308.21 

3.3.3 

90 

5730.00 

49.8 

31 

RAILROAD    CURVES. 


THE    FOLLOWING    TABLE    SHOWS    THE    METHOD    OF 

KEEPING     THE     FIELD     NOTES 

OF  A  SURVEY.  FROM  WHICH  THE  CENTER  LINE   IS  LAID  ON  THE  MAP 


Angle  at  in- 

Course of 
tangent, 

No.  of 
ft.  from 

From 

To 

Length 

Length  of 

tersection 

and 

Radius 

intersec- 

sta- 

sta- 

of tan- 

curves in 

of   tangents 

degree 

of 

tion  of 

tion. 

tion. 

gents  in 

feet 

or  angle  at 

and  direc- 

curves 

tangents 

feet. 

centre. 

tion  of 
curves. 

in  feet. 

to  begng. 
of  curve. 

TangBDt 

7°         24' 

S  19°  21'  E 
3°  42'  L 

0. 

2!    " 



200. 

1548.65 

100.14 

2. 

26. 

2400. 

24°        00' 

1°  00'  R 

5730. 

1217.96 

26. 

43.556 

1755.60 

Tangent 

S     2°  45'  E 

43.556 

61.681 

1812.5 

36°        15' 

2°  00'  R 

2865. 

937.82 

61.681 

93.650 

3196  90 

Tangent 

8  33°  30'  W 

93.650 

102.517 

886.7 

13°       18' 

1°  30'  L 

3820. 

445.37 

102.517 

143.90 

4138.30 

Tangent 

S  20°  12'  W 

143.90 

155.766 

1186.66 

23°        44' 

2°  00'  L 

2865. 

602.02 

155.766 

170.43 

1466.40 

Tangent 

S    3°  32'  E 

170.43 

181.296 

1086.66 

21°        44' 

2°  00'  R 

2865. 

550.00 

181.296 

184.506 

321.00 

T.ingent 

S  18°  12'  W 

184.506 

193.195 

868.89 

13°       02' 

1°  30'  R 

3820. 

436.37 

193.195 

213.064 

1986.9 

T.ingent 

S  31°  14'  W 

213.064 

220.908 

784  44 

11°        46' 

1°  30'  L 

3820. 

393.61 

220.908 

230.546 

963.8 

Tangent 

S  19°  28'  W 

230.546 

242.496 

1195  00 

23°        54' 

2°  00'  R 

2865. 

606.37 

242.496 

252.356 

986  00 

' 

Tangent 

S  43°  22'  W 

252.356 

263.756 

1140.00 

17°       06' 

1°  30'  L 

3820. 

574.30 

263.756 

266.02 

226.40 

Tangent 

S  26°  16'  W 

266.02 

268.02 

200.00 

3° 

1°  30'  L 

3-t20. 

100.05 

268.02 

277.21 

918.89 

27°        34' 

3°         L 

1910. 

468.55 

277.21 

279.21 

200  00 

3°        00' 

1°  30'  L 

3820. 

100.05 

279.21 

289.011 

980.1 

Tangent 

S     7°  18'  E 

289.011 

291.011 

200.00 

3°       00' 

1°  30'  R 

3820. 

100.05 

291.011 

301.422 

1041.10 

31°        14' 

3°  00'  R 

1910. 

53  i.88 

301.422 

303.00 

157.8r, 

2°        22' 

1°  30'  R 

3820. 

78.90 

303.00 

321.0<J 

1800. 

Tangent 

S   29°  18' W 

321.00 

334.00 

1300. 

26° 

2°         L 

2865. 

661.44 

334. 

338.71 

471.00 

Tnngent 

S    3°  18'  W 

338.71 

347.15 

814.1G 

16°        53' 

2°  00'  R 

2865. 

425.19 

347.15 

364.00 

1685.00 

Tangent 

8  20°  11'  W 

364. 

376.633 

1263.33 

37°        54' 

3°          tt 

1910. 

655.80 

376.633 

389.53 

389.70 

Tangent 

8  58°  05'  W 

380.53 

392.38 

1185. 

23°        42' 

2°         R 

2865. 

601.14 

392.38 

402.92 

1054.00 

Tangent 

8  81°  47' W 

402.92 

404.92 

200. 

3°        00' 

1°  30'  L 

3820. 

100.05 

404.92 

418.198 

1327.77 

39°        50' 

3°  00'  L 

1910. 

632.04 

418.198 

420.198 

200. 

Tangent 

8  38°  57'  W 

420.198 

441.002 

2080.41 

83°        13' 

4°          L 

1432. 

1272.21 

441.002 

442.582 

158. 

4°        00' 

2°  32'  L 

2261.87 

79.99 

442.582 

449. 

641.8 
22.262.90 

22.637.31 

Tangent 

8  48°  16'  E 

32  EXCAVATION    AND    EMBANKMENT. 

APPLICATION   OF   THE   PRISMOIDAL    FORMULA 

IN  DETERMINING    THE    QUANTITIES    OF    RAILROADS   AND    CANAL    EXCAVA- 
TIONS  AND  EMBANKMENTS. 


In  order  to  obtain  the  mean  area  from  transverse  sections,  con- 
struct from  the  average  cuttings  and  average  horizontal  distances 
of  the  slopes  of  the  end  section,  a  middle  section ;  and  add  to  four 
times  the  area  of  this  section  the  area  of  the  end  sections,  and  take 
one-sixth  of  the  product  for  the  mean  area. 

The  following  diagrams  show  most  of  the  figures  which  occur  in 
taking  cross  sections  of  railroads,  and  serve  to  illustrate  the  ap- 
plication of  the  formula.  In  practice,  however,  intermediate  sec- 
tions would  be  taken  between  station  0  and  station  1,  and  at  such 
other  points  as  any  sudden  or  material  change  in  the  surface 
would  seem  to  require. 

The  cuttings  and  horizontal  distances  from  the  centre  to  the  ter- 
mination of  the  slopes,  are  set  down  in  tabular  form.  The  notes  of 
the  middle  section  may  at  convenience  be  interlined  in  the  space 
between  the  notes  of  the  end  sections.  From  this  form  the  factors 
for  the  areas  are  made  without  resorting  to  diagrams.— Page  34. 

*It  will  be  seen  by  inspecting  the  diagrams  that  the  embankment 
between  stations  3  and  4  assumes  the  shape  of  a  pyramid,  and  hence 
one-third  of  the  area  of  the  embankment  set  opposite  station  4, 
should  be  multii)lied  by  the  distance  between  stations  3  and  4  to 
obtain  the  quantity.  Between  stations  4  and  5  the  excavation  as- 
sumes the  same  form,  and  should  also  be  calculated  as  a  pyramid; 
or  construct  the  middle  section  as  before  described,  and  calculate 
the  distance  "from  the  centre  to  the  point  where  the  surface  and  the 
grade  intersect ;  and  make  out  the  factors  accordingly. 

Having  obtained  the  mean  areas,  proceed  as  hereinafter  des- 
cribed to  ascertain  the  cubic  yards. 


EXCAVATION    AND    EMBANKMENT. 


33 


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34 


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EXCAVATION    AND    EMBANKMENT. 


35 


-Sr>jA.CiT01ElS. 


EXCAVATION. 

STATION  0.  AREAS. 

0. 0. 0.     =  000. 

MIDDLE  SECTION. 
16.      X     5.  =  80. 
20.      X     6.  =120. 
25.      X     8.  =200. 

400.-^2.=200. 
STATION    1. 
22.      X   10.  =220. 
20.      X   12.  =240. 
40.      X   16.  =640. 


1100.^2.=550. 
MIDDLE  SECTION. 


19,75  X     8.  =158. 

9.50  X  20.  =190. 

32.50  X   12.  =390. 


738.^2.=369. 

STATION    2. 


17.50  X  6.  =105. 
20.  X  7.  =140. 
25.      X     8.  =200. 


445.-=-2.=222.5. 
MIDDLE    SECTION. 
13.75  X     3.  =  41.25 
20.      X     4.5=  90. 
22.      X     6.  =132. 


263.25.-:- 2. 

=131.62 

STATION  3. 

20. 

X 

2.   = 

=  40. 

19. 

X 

4.  = 

=  76. 

116. -=-2.= 

58. 

MIDDLE  SECTION. 

12.8 

X 

1.  = 

=  12.80 

18.25  X 

3.5= 

=  63.88 

17.5 


76.68.-^2.=  38.34. 
STATION    4. 
X     3.  =  52.5  -^2.=  26.25. 
STATION    5. 


-0. 


19. 


19. 
15. 


19. 
20. 


20.5 

20. 

16. 


16. 
20. 
16. 


EMBANKMENT. 


STATION  4. 


ABEAS. 


X      5. 


95.-r-2.=  47.5. 


MIDDLE  SECTION. 

<  5.5=104.5 

<  1.  =  15. 


119.5-T-2. 
STATION    5. 


59.75. 


=114. 
=  40. 

154.-T-2.=  77. 


MIDDLE  SECTION. 

X     7.  =143.5 
X     5.  =100. 
X     4.  =  64. 


307.5-^2.=153.75. 
STATION  6. 


22.  X  8.  =176. 
20.  X  8.  =160. 
22.      X     8.  =176. 


512.-=-2.=256. 

MIDDLE  SECTION. 

X  4.  =  64. 
X  4.  =  80. 
X     4.  =  64. 


208.-^2=104. 
STATION    7. 

0. 0. 


36 


EXCAVATION  AND  EMBANKMENT. 


The  cubic  yards  between  station  0  and  station  1  according  to 
the  method  of  adding  the  end  areas  and  taking  one-half  for  the 
mean  area  -  -       •  .         =  ioi8.51  c.  yds.    |    c.  yds. 

By  2d  (or  Prismoidal  method)=  833.33       "       i  185.18 

**  1st  method  between  station  1  and  2  =  1430.55       " 


"2d 

Ist 
2d 

'Ist 
2d 

1st 
2d 
Error  on 


land  2 

2  and  3 

2  and  3 

3  and  4 

3  and  4 

4  and  5 
4  and  5 


1387.96 

519.44 
498.14 

156.01 
146.66 

48.59 
32.40 


500   lineal   feet  of  excavation 


42.59 

21.30 

9.35 

16.19 
=274.61 


There  are  other  methods  which  approximate  nearer  than  the 
averaging  method.  For  instance,  taking  ^^ths  of  tlie  difference 
between  the  end  areas,  (or  tne  difference  0x0.46j  and  adding  it  to 
the  lesser  end  area  for  the  mean. 

This  method  approximates  nearer  the  true  quantity.  The  prin- 
cipal discrepancy  occurs  where  the  embankment  assumes  the 
wedge  or  pryamidal  form.— 


By  3d   method  between  station  0  and  1 
"       (or  Prismoidal)  0  and  1 


2d 

"3d 
"2d 

"3d 

"2d 

"3d 
"2d 

"3d 

"2d 


937.03   I    cubic  yards. 
833.33   f   -I- 


between  station  1  and  2 
1  and  2 


2  and  3 

2  and  3 

3  and  4 

3  and  4 

4  and  5 
4  and  5 


1382.03  ) 

1387.96  I' 

495.08  t 

498.14  f 

151.31  I 

146.66  f 

44.72  ) 

32.40  f 


+ 


Error  on  500  lineal  feet  of  excavation 


103.70 
5.93 

3.06 

4.65 

12.32 

111.68 


Another  method  is  to  multiply  J  of  the  distance  between  trans- 
verse sections,  by  the  sum. of  the  end  areas,  added  to  four  times 
half  their  sum  ;  and  dividing  by  27  for  the  cubic  yards. 

The  results  are  the  same  as  by  the  first  method  except  between 
stations  0  and  1. 


EXCAVATION  AND  EMBANKMENT.  87 


EXPLANATION  OF  THE  FOLLOWING  TABLES. 

The  tables  are  calculated  for  a  distance  of  100  feet  between  trans- 
verse sections. 

In  the  left  hand  column  are  given  the  areas  in  feet.  To  obtain  the 
cubic  yards  for  areas,  without  decimals,  look  in  the  second 
column  under  the  head  of  0,  and  opposite  the  given  area,  find  the 
cubic  yards. 

Example. — Required  the  number  of  cubic  yards  for  an  area  of 
190  feet.  In  the  second  column,  under  the  head  of  0,  and  opposite 
190  in  the  first  column,  find  703.70  cubic  yards. 

To  obtain  the  cubic  yards  for  a  less  distance  than  100  feet,  multi- 
ply the  cubic  yards  found  in  the  tables  by  the  given  distance,  and 
point  off  the  fractional  parts  of  100  feet. 

If  the  area  has  decimal  j)arts,  pass  the  eye  to  the  right,  opposite 
the  area  of  the  whole  number,  and  under  the  head  of  such  decimal 
will  be  found  the  number  of  yards. 

Example.— Required  the  cubic  yards  for  an  area  of  105.4  feet.  In 
the  sixth  column,  under  the  head  of  40,  and  opposite  105  in  the  first 
column,  are  given  390,37  cubic  yards. 

If  the  yards  for  an  area  greater  than  359.90,  and  not  exceeding 
3599  feet,  are  required,  the  decimal  point  of  the  area  given  in  the 
tables,  and  that  of  the  cubic  yards,  being  removed  one  figure  to  the 
right,  will  give  the  required  yards.  If  there  are  decimal  parts,  add 
the  cubic  yards  found  opposite  0  in  the  first  column,  under  the 
head  of  such  decimal. 

Example.— Required  the  cubic  yards  for  an  area  of  1975  feet;  re- 
move the  decimal  point  one  figure  to  the  left,  and  find  the  yards  for 
an  area  of  197.5  feet  =  731.48,  then  remove  the  decimal  point  one 
figure  to  the  right  and  you  have  7314.8  cubic  yards.  If  there  is  a 
decimal,  add  the  cubic  yards  found  for  such  decimal. 

Or,  to  obtain  the  cubic  yards  for  an  area  exceeding  3599  feet,  take 
one  half  of  the  area,  and  seek  the  corresponding  yards  in  tables 
and  multiply  the  same  by  '2. 


38 


EXCAVATION    AMD    EMBANKMENT    TABLES 

1  0.00  1  0.10  1  0.20  1  0.30  1  0.40  |  0.50  |  0.60  |  0.70 

0.80 

0.90 

0 

0.00 

0.37 

0.74 

1.11 

1,48 

1.85 

2.22 

2.59 

2.96 

3.33 

1 

3.70 

4.07 

4.45 

4.81 

5.19 

5.56 

5.93 

6.;t0 

6.67 

7.04 

2 

7.41 

7.78 

8.15 

8.52 

8.89 

9.26 

9.63 

10.00 

10.37 

10.74 

3 

11.11 

11.48 

11  .'85 

12.22 

12.59 

12.96 

1:3.33 

13.70 

14.07 

14.44 

I 

14.82 

15.19 

15.66 

15.93 

16.30 

16.67 

17.04 

17.41 

17.78 

18.16 

5 

18.52 

18.89 

19.26 

19.63 

20.00 

20.37 

20.74 

21.11 

2:. 48 

21.86 

6 

22.22 

2:2.59 

22.96 

23.33 

23.70 

24.07 

24.44 

24.82 

25.19 

25.56 

7 

25  93 

26.30 

26.67 

27.04 

27.41 

27.78 

28.15 

28.52 

28.89 

29.26 

8 

29  63 

30.00 

30.37 

30.74 

31.11 

31.48 

31.85 

32.22 

32.59 

32.96 

9 

33.33 

33.70 

34.07 

34.44 

34.82 

35.19 

35.56 

35.93 

36.30 

36.67 

10 

37.04 

37.41 

37.78 

38.15 

38.52 

38.89 

39.26 

b9.63 

40.00 

40.37 

11 

40  74 

41.11 

41.48 

41.85 

42.22 

42.59 

42.96 

4!.33 

43.70 

44.07 

12 

44.44 

44.82 

45.19 

45.56 

45.93 

46.30 

46.67 

47.04 

47.41 

47.78 

13 

48.15 

48.52 

48.89 

49.26 

49.63 

50.00 

50.:i7 

50.74 

61.11 

51.48 

14 

5185 

52.22 

52.59 

62.96 

5:;.33 

53.70 

54.07 

51.44 

54  82 

55.19 

15 

65.56 

55.93 

56.30 

56.67 

57.04 

57.41 

57.78 

58.15 

58.52 

58.89 

16 

59  26 

69.63 

60.00 

60.37 

60.74 

61.11 

61.48 

61.' 5 

62.22 

62.59 

17 

62.96 

63.33 

63.70 

64.07 

64.4-1 

64.82 

65.19 

65.56 

65.93 

66.30 

18 

66.67 

67.04 

67.41 

67.78 

68.15 

68.52 

68.89 

69.26 

69.63 

70.00 

19 

70.37 

70.74 

71.11 

71.48 

71.85 

72.22 

72..59 

72.96 

7:3.33 

73  70 

20 

74.07 

74  44 

74  82 

75.19 

75.56 

75.93 

76.30 

76.67 

77.04 

77.41 

21 

77.78 

78.15 

78.52 

78.89 

79.26 

79.63 

80.00 

80.37 

80.74 

81.11 

22 

81.48 

81.85 

82.22 

82.59 

82.96 

8:i.33 

83.70 

*1.07 

84.44 

84  82 

23 

85.19 

85.56 

85.93 

86.30 

86.67 

87.04 

87.41 

87.78 

88.15 

88.52 

21 

88.89 

89.26 

89  63 

90.00 

90.37 

90.74 

91.11 

91.48 

91.85 

92.22 

26 

92.59 

92  96 

93.33 

93.70 

94.07 

94.44 

94.82 

95.19 

95.56 

95.93 

26 

96.30 

96.67 

97.01 

97.41 

97.78 

98.13' 

98.52 

98.«9 

99.26 

99  63 

27 

100.00 

100.37 

100.74 

101.11 

101.48 

101.85 

102.22 

102.59 

102.96 

103.33 

28 

103.70 

104.07 

104.44 

104.82 

105.19 

105.56 

105.93 

106.30 

106.67 

107.04 

29 

107.41 

107.78 

108.15 

108-52 

108.89 

109.26 

109.63 

110.00 

110.37 

110.74 

30 

111.11 

111.48 

111.85 

112.22 

112.59 

112.96 

113.33 

113.70 

114.07 

114.44 

31 

114.81 

115.18 

115  56 

115.92 

116.29 

116.67 

117.03 

117.40 

117.77 

118.15 

32 

118.52 

118.89 

119.26 

119.63 

120.00 

120.37 

120.74 

121.11 

121.48 

121.86 

33 

122  22 

122  59 

122.96 

1'23.33 

123.70 

124.07 

124.44 

124.81 

125.18 

125.55 

U 

125.92 

126.30 

126.66 

127.03 

127.40 

127.77 

128.14 

128  51 

128.R8 

129.26 

35 

129.63 

130  00 

1.30  37 

130.74 

131.11 

131.48 

131.85 

132.22 

132.59 

132.96 

36 

133.33 

133.70 

134.07 

134.44 

134.81 

135.18 

135.55 

135  92 

136.29 

136.67 

37 

137  04 

1S7.41 

137.78 

138.15 

138.52 

138.89 

139.26 

139.63 

140.00 

140  37 

38 

140.74 

141.il 

141.48 

141.85 

142.22 

142.59 

142.96 

143.33 

143.70 

144.07 

39 

144.44 

141.81 

145.18 

145-55 

145.92 

146.29 

146.66 

147.03 

147.40 

147.78    ' 

40 

148.15 

14S.52 

148.89 

149.26 

149.63 

150.00 

150.37 

161.74 

151.11 

151.48 

41 

151.85 

152.22 

152.59 

152-96 

15:1.33 

153.70 

154.07 

154.44 

154.81 

155  18    [ 

42 

155.55 

155.92 

156.29 

156-66 

157.03 

157.40 

157.77 

15S.14 

158.51 

158.89 

43 

159.26 

159.63 

160  00 

160.37 

160.74 

161.11 

161.48 

161.85 

162.22 

16259 

44 

162.96 

163.33 

163.70 

164.07 

164.44 

164.81 

165.18 

165.55 

165.92 

166.:?0 

45 

166.67 

167  04 

167.41 

167.78 

168.15 

168.52 

168.89 

169.26 

169.63 

17000 

46 

170.37 

170.74 

171.11 

171.48 

171.85 

17-'.22 

172.59 

172.96 

173.33 

17:3.70 

47 

174.07 

174.44 

174.81 

175.18 

175.55 

175.92 

176.29 

176.66 

177.03 

177.41 

48 

177.78 

178.15 

178.52 

178-89 

179.26 

179.63 

180.00 

180.:, 7 

180.74 

181.11 

49 

181.48 

181.85 

182.22 

182-5* 

182.96 

183.33 

18:i.70 

184.07 

184.44 

184.81 

50 

185.18 

185.55 

185  92 

186-29 

186.66 

187.03 

187.40 

187.77 

188.14 

18852 

51 

188.89 

189.26 

189.63 

190-00 

190.37 

190.74 

191.11 

191.48 

191.85 

192.22 

62 

192  59 

192.96 

193.33 

193-70 

194.07 

194.44 

194.81 

195.18 

195.55 

195.93 

53 

196.30 

196.67 

197.04 

197-41 

197.78 

198.15 

198.52 

198  89 

199.26 

199  6.3 

64 

200.00 

200.37 

200.74 

201-11 

201.48 

201.85 

202.22 

202.59 

202.96 

203.3:3 

55 

203.70 

204.07 

204.44 

204.81 

205.18 

205.55 

205.92 

206  29 

206.66 

207.03 

56 

207.41 

207.78 

208  15 

208.52 

208.89 

209.26 

209.63 

210  fK) 

210.37 

210.74 

57 

211.11 

211.48 

211.85 

212.22 

212.59 

212.96 

21:i.3:< 

21:1.70 

214.07 

214.44 

68 

214.81 

215.1<1 

215.55 

215.92 

2 '0.29 

216.66 

217.03 

217.40 

217.77 

218.15 

69 

218.62 

218.89 

219.26 

219.63    220.00 

220.37  i  220.74 

221.11 

221.48 

221.S-5 

39 


EXCAVATION    AND    EVIBANKMEST    TABLES. 

JO.OO  1  0.10  |0.20  |0.30  i0.40  |  0.50  |  0.60  |  0.70 

0.80    |0.90 

60 

222.22 

222.59 

222.96 

223.33 

223.70 

224.07 

224.44 

224.81 

225.18 

225.55 

61 

225.92 

226.29 

226.66 

227.03 

227.40 

227.77 

2.-8,14 

228.51 

228.88 

229.26 

62 

229.63 

230.00 

230.37 

230.74 

231.11 

231.48 

2.31,85 

232.22 

232.59 

232.96 

6J 

233.33 

233.70 

•.J34.07 

234.44 

234.81 

235.18 

2.35,55 

235.92 

236.29 

236.67 

64 

237.04 

2i7.41 

237.78 

238.15 

238.52 

238,89 

239.26 

239.63 

240.00 

240.37 

65 

240.74 

241.11 

241.48 

241.85 

242.22 

242.59 

242.96 

243.3S 

243.70 

244.07 

66 

244.44 

244.81 

245.18 

245.55 

245.92 

246.30 

246.67 

247.04 

247.41 

247,78 

67 

248.15 

248.52 

248.89 

249.26 

249.63 

250.00 

250.37 

250.74 

251.11 

251.48 

6S 

251.85 

252.22 

252.59 

252.96 

253.33 

253.70 

254.07 

254.44 

254.81 

255.18 

69 

255.56 

255.93 

256.30 

256.67 

257.04 

257.41 

257.78 

258.15 

258.52 

258.89 

70 

259.26 

259.63 

260.00 

260,37 

260.74 

261.11 

261.48 

261.85 

262.22 

262.59 

71 

262.96 

263.33 

263.70 

264.07 

264.44 

264.81 

265.18 

265.55 

265.92 

266.30 

72 

266.67 

267.01 

2117.41 

267.78 

268.15 

268.52 

268.89 

269.26 

269.63 

270.00 

73 

270.37 

270.74 

271.11 

271.48 

271.85 

272.22 

272.59 

272.96 

273.33 

273.70 

74 

274.07 

274.44 

274.81 

275.18 

275.55 

275.92 

276.29 

276.66 

277.04 

277.41 

75 

277.78 

278.15 

278.52 

278.89 

279.26 

279.63 

280.00 

280.:i7 

280.74 

281.11 

76 

281.48 

281.85 

282.22 

282.59 

282.96 

283.33 

283.70 

284.07 

284.44 

284.81 

77 

285.18 

285.56 

285.93 

286.30 

286.67 

287.04 

287.41 

287.78 

288.15 

288,52 

78 

288.89 

289.26 

289.G3 

290.00 

290.37 

290.74 

291.11 

291.48 

291.85 

292.22 

79 

292.59 

292.96 

293.33 

293.70 

294.07 

294.44 

29J.81 

295.18 

295.55 

295,93 

80 

296.30 

296.67 

297.04 

297.41 

297.78 

298.15 

298.52 

298.89 

299.26 

29i),63 

1      81 

300.00 

300.37 

300.74 

301.11 

301.48 

301.85 

302.22 

302.59 

302.96 

303.33 

82 

303.70 

304.07 

304.44 

3U4.81 

305.18 

305.55 

305.92 

306.29 

306.66 

307.03 

83 

307.41 

307.78 

308.15 

308.f'2 

308.89 

309.26 

309.63 

310,00 

310.37 

310,74 

84 

311.11 

311.48 

311.85 

312.22 

312.59 

312.96 

313.33 

313.70 

314.07 

314.44 

85 

314.81 

315.19 

315.56 

315.93 

316.30 

316.67 

317.04 

317.41 

317.78 

318,15 

86 

318.52 

318.89 

319.26 

319.63 

320.00 

320.37 

320.74 

321.11 

321.18 

.321. ^5 

87 

322.22 

322.59 

322.96 

323.33 

323.70 

324.07 

324.44 

324.81 

325.18 

325  55 

88 

325.92 

326.30 

326.67 

327.04 

327.41 

327.78 

328.15 

328.52 

328.89 

329.  .6 

89 

329.63 

330.00 

330.37 

330.74 

331.11 

331.48 

331.85 

332.22 

332.59 

332.96 

90 

333.33 

333.70 

334.07 

334.44 

334.81 

335.18 

335.55 

335.92 

336.29 

336.67 

91 

337.04 

337.41 

337.78 

338.15 

338.52 

338.89 

339.25 

339.62 

339.99 

310.37 

>  92 

340.74 

341.11 

341.48 

341.85 

342.22 

342.59 

342.96 

343.33 

343.70 

344.07 

93 

344.44 

344.81 

345.18 

345.56 

345.93 

346.30 

346.67 

347.03 

347.40 

317.78 

94 

348.15 

348.52 

348.89 

349.26 

349.63 

350.00 

350.37 

350.74 

351.11 

351.48 

95 

351.85 

352.22 

352.59 

352.116 

353.33 

353.70 

354.07 

354.44 

354.81 

355.18 

96 

355.55 

355.93 

356.30 

356.67 

357.04 

357.41 

357.78 

358.15 

358.52 

358  89 

97 

359.26 

359.63 

360.00 

360.37 

360.74 

361.11 

361.48 

361.85 

362.22 

362.59 

98 

362.9(5 

363.33 

363.70 

364.07 

364.44 

364.81 

365.18 

365.55 

365.93 

366.30 

99 

366.67 

367.04 

367.41 

367.78 

368.15 

368.52 

368.89 

369.26 

369.63 

370.00 

100 

370.37 

370.74 

371.11 

371.48 

371.85 

372.22 

372.59 

372.96 

373.33 

373.70 

101 

374.07 

374.44 

374.81 

375.1S 

375.55 

375.92 

376.29 

376.67 

377.04 

377.41 

102 

377.78 

378.15 

378.52 

378.89 

379.26 

379.63 

380.00 

380.37 

380.74 

381.11 

103 

381.48 

381.85 

382.22 

382.59 

382.96 

3H3.33 

383.70 

384.07 

384.44 

384  81 

104 

385.18 

385.55 

385.92 

386.29 

386.67 

387.04 

387.41 

387.78 

388.15 

388.52 

105 

388.89 

389.26 

389.63 

390.00 

390.37 

390.74 

391,11 

391.48 

391.85 

392.22 

106 

392.59 

392.96 

393.33 

393.70 

394.07 

394.44 

394,81 

395.18 

395.55 

395.92 

107 

396.30 

396.<>7 

397.04 

397.41 

397.78 

398.15 

398,52 

398.89 

399.26 

399.63 

108 

400.00 

400.37 

400.74 

401.11 

401.48 

401.85 

402,22 

402.59 

402.96 

403.33 

109 

403.70 

404.07 

404.44 

404.81 

405.18 

405.55 

405,92 

406,29 

406.67 

407.04 

110 

407.41 

407.78 

408.15 

408.52 

408.89 

409.26 

409,63 

410.00 

410.37 

410.74 

111 

411.11 

411.48 

411.85 

412.22 

412.59 

412.96 

413,33 

413.70 

414.07 

414.44 

112 

414.81 

415.18 

415.55 

415.92 

416.29 

416.67 

417,04 

417.41 

417.78 

418.15 

j     113 

418.52 

418.89 

419.26 

419.63 

420.00 

420.37 

420,74 

421.11 

421.48 

421.85 

114 

422.22 

422.59 

422.96 

423.33 

423.70 

424.07 

424,44 

424.81 

425.18 

425.56 

115 

425.93 

426.30 

4i6.G7 

427.04 

427.41 

427.78 

428,15 

428.52 

428.89 

429.26 

116 

429.63 

430.00 

430.37 

430.74 

431.11 

431.48 

431,85 

432.22 

432.59 

432.96 

117 

433.33 

433.70 

4;i4.07 

434.44 

434.81 

435.18 

435.55 

435.92 

436.29 

436.67 

118 

437.04 

437.41 

437.78 

438.15 

438.52 

438.89 

439.26 

439.63 

440.00 

440.37 

119 

440.74 

441.11 

441.48 

441.85 

442.22 

442.59 

442,96 

443,33 

•  443.70 

414.07 

40 


EXCAVATION   AND    EMBANKMENT    TABLES. 

" 

1  0.00   1  0.10   j  0.20  1  0.30  1  0.40   |  0.50  j  0.60   |  0.70 

0.80     0.90 

120 

444.44 

444.81 

445.18 

445.55 

445.92 

446.29 

446  67    447  04 

447.41 

447.78 

121 

448.15 

448.52 

448.89 

449.26 

449.63 

450.00 

450.37 

450.74 

451.11 

451.48 

122 

451.85 

452.22 

452.59 

462.96 

453.33 

453.70 

454.07 

454.44 

454.81 

455.18 

123 

455.55 

455.92 

466.29 

466.67 

457.04 

457.41 

457.78 

458.15 

458.52 

458.89 

124 

459.26 

459.63 

460.00 

460.37 

460.74 

461.11 

461.48 

461.85 

462.22 

462.59 

125 

462.96 

463.33 

463.70 

464.07 

464.44 

464.81 

465.18 

465.55 

465.93 

466  30 

126 

466.67 

467.04 

467.41 

467.78 

468.15 

468.52 

468.89 

469.26 

469.63 

470.00  , 

127 

470.37 

470.74 

471.11 

471.48 

471.85 

472.22 

472.59 

472.96 

473.33 

473.70 

128 

474.07 

474.44 

474.81 

475.18 

475.56 

475.93 

476.30 

476.67 

477.04 

477.41 

1?9 

477.78 

478.15 

478.52 

478.89 

479.26 

479.63 

480.00 

480.37 

480.74 

481.11 

130 

481.48 

481.85 

482.22 

482.59 

482.96 

483.33 

483.70 

484.07 

484.44 

484.81 

131 

485.18 

485.55 

485.92 

486.29 

486.67 

487.04 

487.41 

487.78 

488.15 

488.52 

132 

488.89 

489.26 

489.63 

490.00 

490.37 

490.74 

491.11 

491.48 

491.85 

492.22 

.133 

492.59 

492.96 

493.33 

493.70 

494.07 

494.44 

494.81 

495.19 

495.56 

495.93 

134 

496.30 

496.67 

497.04 

497.41 

497.78 

498.15 

498.52 

498.89 

499.26 

499.63 

135 

500.00 

500.37 

600.74 

501.11 

501.48 

501.85 

502.22 

502.59 

502.96 

503.33 

136 

603.70 

504.07 

504.44 

504.81 

505.18 

505.56 

505.93 

606.30 

506.67 

507.04 

137 

607.41 

507.78 

608.15 

508.52 

508.89 

509.26 

509.63 

510.00 

510.37 

510.74 

138 

511.11 

511.48 

511.85 

512.22 

612.59 

512.96 

513.33 

513.70 

514.07 

614.44 

139 

514.81 

515.18 

516.65 

615.92 

516.29 

516.67 

617.04 

517.41 

517.78 

618.16 

140 

518.52 

518.89 

519.26 

519.63 

520.00 

520.37 

520.74 

521.11 

521.48 

521.85 

141 

522.22 

622.59 

622.96 

623.33 

623.70 

524.07 

524.44 

524.81 

525.19 

525.56 

142 

525.93 

526.30 

526.67 

627.04 

527.41 

527.78 

528.15 

528.52 

528.89 

529.26 

143 

529.63 

630.00 

530.37 

630.74 

531.11 

531.48 

531.85 

532.22 

532.59 

532.94 

144 

533.33 

633.70 

634.07 

634.44 

534.81 

535.18 

535.56 

535.93 

536-30 

536.67 

145 

537.04 

5:!7.41 

637.78 

638.15 

538.52 

538.89 

539.26 

539.63 

540.00 

540.37 

146 

540.74 

541.11 

541.48 

641.85 

542.22 

542.59 

542.96 

543.33 

543.70 

644.07 

147 

544.44 

544.81 

646.18 

545.56 

545.93 

546.30 

546.67 

547.04 

547.41 

547.78 

148 

548.15 

548.52 

648.89 

549.26 

649.63 

550.00 

550.37 

550.74 

551.11 

551.48 

149 

551.85 

552.22 

552.59 

652.96 

553.33 

553.70 

554.07 

554.44 

554.81 

555.18 

150 

55555 

655.93 

556.30 

556.67 

657.04 

557.41 

557.78 

558.15 

558.52 

558.89 

151 

559.26 

659.63 

660.00 

660.37 

660.74 

561.11 

561.48 

561.85 

562.22 

662.59 

152 

662.96 

663.33 

663.70 

664.07 

564.44 

564.81 

565.18 

565.56 

565.93 

566.30 

153 

666.67 

567.04 

667.41 

667.78 

568.15 

568.52 

568.89 

569.26 

569.63 

570.00 

154 

570.37 

570.74 

571.11 

571.48 

571.85 

572.22 

572.59 

672.96 

573.33 

573.70 

155 

674.07 

574.44 

574.81 

575.18 

575.56 

575.93 

676.30 

576.67 

577.04 

577.41 

156 

577.78 

578.15 

578.52 

578.89 

679.26 

579.63 

580.00 

580.37 

580.74 

681.11 

157 

681.48 

581.85 

582.22 

682.59 

582.96 

5«3.33 

583.70 

684.07 

584.44 

684.81 

158 

585.18 

585.55 

686.92 

686.29 

686.66 

587.04 

6S7.41 

587.78 

588.15 

588.52 

159 

588.89 

589.26 

589.63 

590.00 

590.37 

590.74 

591.11 

591.48 

591.85 

592  22 

160 

592.59 

592.96 

5^3.33 

593.70 

594.07 

594.44 

594.81 

595.18 

595.55 

595.92 

161 

596.29 

696.67 

597.04 

697.41 

697.78 

598.16 

598.52 

598.89 

599.26 

599.63 

162 

600.00 

600.37 

600.74 

601.11 

601.48 

601.85 

602.22 

602.59 

602.% 

603.33 

163 

603.70 

604.07 

604.44 

604.81 

605.18 

606.55 

605.92 

606.30 

606.67 

607.04 

164 

607.41 

607.78 

608.15 

608.52 

608.89 

609.26 

609.63 

610.00 

610.37 

610.74 

165 

611.11 

611.48 

611.85 

612.22 

612.59 

612.96 

613.33 

613.70 

614.07 

614.44 

166 

614.81 

615.18 

615.55 

615.92 

616.29 

616.67 

617.04 

617.41 

617.78 

618.15 

167 

618.52 

618.89 

619.26 

619.63 

620.00 

620.37 

620.74 

621.11 

621.48 

621.85 

168 

622.22 

622.59 

622.96 

623.33 

623.70 

624.07 

624.44 

624.81 

625.18 

625.56 

169 

626.93 

626.30 

626.67 

627.04 

627.41 

627.78 

628.15 

628.52 

628.89 

629.26 

170 

629-63 

630.00 

630.37 

650.74 

631.11 

631.48 

631.85 

632.22 

632.59 

632.96 

171 

633.33 

633.70 

634.07 

634.44 

6;14.81 

635.18 

635.55 

635.92 

636.29 

636.66 

172 

637.04 

637.40 

637.77 

63814 

638.51 

638.88 

639.25 

639.62 

639.99 

640.37 

173 

640.74 

641.11 

641.48 

641.85 

642.22 

642.59 

642.96 

643.33 

643.70 

644.07 

174 

644.44 

644.81 

645.18 

645.55 

645.92 

646.29 

646.66 

647.03 

647.41 

647.78 

175 

648.15 

648.52 

648.89 

649  26 

649.63 

f.50.00 

650.37 

650.74 

651.11 

651.48 

176 

651.8.5 

652.22 

652.59 

652.96 

653.33 

653.70 

654.07 

654.44 

654.81 

655.18 

177 

655.66 

655.93 

65fi.H0 

656.67 

657.04 

657.41 

657.78 

658.15 

658.52 

658.89 

17H 

659.26 

659.63 

660.00  1  660.37 

1  660.74 

661.11 

661.48 

66185 

662  22 

662.69 

179 

66-2.% 

663.33 

C63.70  1  664.07 

664.44 

664.81    '  665.13 

665.55 

665.92 

666.29 

41 


EXCAVATION    AND  EMBANKMENT   TABLES. 

1  0.00  1   0.10  1  0.20  1  0.30  1   0.40  |   0.50  j   0.60  |  0.70  |  0.80 

1    0.90 

180 

066.67 

667.04 

667.41 

607.78 

668.15 

068.52 

668.89 

669.26 

669.63 

670.00 

181 

670.37 

670.74 

671.11 

671.48 

671.85 

672.22 

672.59 

672.96 

673.33 

673.70 

182 

674.07 

674,44 

674.81 

675.18 

675.55 

675.93 

676  30 

676.67 

677.04 

677.41 

183 

677.78 

678.15 

678.52 

678.89 

(•,79.26 

679.63 

680.00 

680.37 

680.74 

681.11 

184 

681.48 

681.85 

682.22 

682.59 

682.96 

683.33 

684.70 

684.07 

684.44 

684.81 

185 

685.18 

685.56 

685.93 

686  30 

686.67 

687.0 i 

687.41 

687.78 

688.15 

688.52 

186 

688.89 

689.26 

689.63 

690.00 

690.37 

690.74 

691.11 

691.48 

691.85 

692.22 

187 

692.59 

692.96 

693.33 

693  70 

694.07 

694.44 

694.81 

695.18 

695.55 

695.92 

188 

696.30 

696.07 

697.04 

697.41 

697.78 

698.15 

698.52 

698.89 

699.26 

699.63 

189 

700.00 

700.37 

700.74 

701.11 

701.48 

701.85 

702.22 

702.59 

702.96 

703.33 

190 

703.70 

704.07 

704.44 

704.81 

705.18 

705.55 

705.92 

706.29 

706.66 

707.03 

191 

707.40 

707.77 

708.14 

708.51 

708.89 

709.26 

709  63 

710.00 

710.37 

710.74 

192 

711.11 

711.48 

711.85 

712  22 

712.59 

712.96 

713.33 

713.70 

714.07 

714.44 

193 

714.81 

715.18 

715.55 

715.92 

716.29 

716.07 

717.04 

717.41 

717.7K 

718.15 

194 

718.52 

718.89 

719.26 

719.63 

720  00 

720.37 

720.74 

721.11 

721.48 

721.85 

195 

722.22 

722.59 

722.96 

723.33 

723.70 

724.07 

724.44 

724.81 

725.18 

725.55 

196 

725.92 

726.29 

726.66 

727.03 

727.40 

727.77 

728.14 

728.51 

728.88 

729.25 

197 

729.63 

730.00 

730.37 

730.74 

731.11 

731.48 

731.85 

732.22 

732.59 

732.96 

198 

733.33 

733.70 

734.07 

734.44 

734.81 

735.18 

735.55 

7.35.93 

736.30 

736.67 

199 

737.04 

737.41 

737.78 

738.15 

738.52 

738.89 

739.26 

739.63 

740.00 

740.37 

200 

740.74 

741.11 

741.48 

741.85 

7-42.22 

742.59 

742.96 

743.33 

743.70 

744.07 

201 

744.44 

744.81 

745.18 

745  55 

745.93 

746.30 

746.67 

747.04 

747.41 

747.78 

202 

748.15 

748.52 

748.89 

749.  6 

"49.63 

750.00 

750.37 

750.74 

751.11 

751.48 

203 

751.85 

752.22 

752.59 

752.96 

753.33 

753.70 

754.07 

754.44 

754.81 

755.18 

204 

755.55 

755.93 

756.30 

756.67 

757.04 

757.41 

757.78 

758.15 

758.52 

758.89 

205 

759.26 

759.63 

760.00 

760.37 

760.74 

761.11 

761.48 

761.85 

762.22 

762.59 

206 

762.96 

763.:(3 

763.70 

764.07 

764.44 

764.81 

765.18 

765.55 

765.93 

766.30 

207 

766.66 

767.04 

767.41 

767.78 

768.15 

768.52 

768  89 

769.26 

769.63 

770.00 

208 

770.37 

770.74 

771.11 

771.48 

771.85 

772.22 

772.59 

772.96 

773.33 

773.70 

209 

774.07 

774.44 

774.81 

775.18 

775.55 

775.93 

776.30 

776.06 

777.04 

777.41 

210 

777.78 

778.15 

778.52 

778.89 

779.26 

779.63 

780.00 

780.37 

780.74 

781.11 

211 

781.48 

781.85 

782.22 

782  59 

782.96 

783.33 

783.70 

784.07 

784.44 

784.81 

212 

785.18 

785.55 

785.93 

786  30 

786.66 

787.04 

787.41 

787.78 

788.15 

788.52 

213 

788.89 

789.26 

789.63 

790.00 

790.37 

790.74 

79111 

791.48 

791.85 

792.22 

214 

792.59 

792.96 

793.33 

793.70 

794.07 

794.44 

794.81 

795.18 

795.55 

795.93 

215 

796.30 

796.66 

797.04 

797.41 

797.78 

798.15 

798.52 

798.89 

799.26 

799.63 

216 

800.00 

800.37 

800.74 

801  11 

801.48 

801.85 

80222 

802.59 

802.96 

803.33 

217 

803.70 

804.07 

804.44 

804  81 

805.18 

805.55 

805.93 

806.30 

806.66 

807.04 

218 

807.41 

807.78 

808.15 

808.52 

808.89 

809.26 

809  63 

810.00 

810.37 

810.74 

219 

811.11 

811.48 

811.85 

812.22 

812.59 

812.96 

813.33 

813.70 

814.07 

814.44 

220 

814.81 

815.18 

815.55 

815.93 

816.30 

816.66 

817.04 

817.41 

817.78 

818.15 

221 

818.52 

818.89 

819.26 

819  63 

8.0.00 

820.37 

820.74 

821.11 

821.48 

821.85 

222 

822.22 

822.59 

822.96 

823.33 

823.70 

824.07 

824.44 

824.81 

825.18 

825.55 

223 

825.93 

826.30 

826.66 

827.04 

827.41 

827.78 

828.15 

828.52 

828.89 

829.26 

224 

829.63 

830.00 

830.37 

830.74 

831.11 

831.48 

831.85 

832.22 

832.59 

832.96 

225 

833.33 

833.70 

834.07 

834.44 

834.81 

8:15.18 

835  55 

835.93 

836.30 

836.66 

226 

837.04 

837.41 

837.78 

838  15 

838.52 

838.89 

839  26 

839.63 

840.00 

840.37 

227 

840.74 

841.11 

841.48 

841.85 

842.22 

842.59 

842.96 

843.33 

843.70 

844.07 

228 

844.44 

844.81 

845.18 

845.55 

845.9! 

846.30 

846  66 

847.04 

847.41 

847.78 

229 

848.15 

848.52 

848.89 

849.26 

849.63 

850.00 

850.37 

8,50.74 

851.11 

851.48 

230 

851.85 

852.22 

852.59 

852.96 

853.33 

853.70 

854.07 

854.44 

854.81 

855.18 

231 

855.55 

855.93 

856.30 

856.66 

857  04 

857.41 

857  78 

858.15 

858.52 

858.89 

232 

859.26 

859.63 

860.00 

860  37 

860.74 

861.11 

861.48 

861.85 

862.22 

862.59 

233 

862.96 

863.33 

863.70 

804  07 

864.44 

864.81 

865.18 

8(';5.i55 

865.93 

866.30 

234 

866.66 

867.04 

867.41 

867.78 

868.15 

868.52 

868.89 

869.26 

869.63 

870  00 

235 

870.37 

870.74 

871.11 

871  48 

871.85 

872.22 

872.59 

872.96 

873.33 

873.70 

236 

874.07 

874.44 

874.81 

875.18 

875.55 

875.93 

876.30 

876.66 

877.04 

877.41 

237 

877.78 

878.15 

878.52 

878.89 

879.26 

879.63 

880.00 

880.37 

880  74 

1   881.11 

238 

881.48 

8^1.85 

882.22 

882.59 

882  96 

883.33 

883  70 

884.07 

884.44 

884.81 

239 

885.18 

885.55 

885.93 

886.30 

880.66 

887.04 

887.41 

887.78 

888.15 

'    888.52 

i-z 


EXCAVATION    AND    EMBANKMENT    TABLES. 

A 

0.00 

0.10   1 

889.26 

0.20  1 

0.30 

0,40  1  0.50  1    0.60 1    0.70  |   0.80    |  0,90 

240 

888.88 

889.63 

890.00 

890,37  .  890.74  !  891,11  I    891.48  i 

891.85 

892.22 

211 

892.59 

892.96 

893.33 

893.70 

894,07 

894.11 

891.81 

8^5.18 

895.55 

895.93 

212 

896.30 

896.66 

897.01 

897.41 

897.78 

898.15 

h9:^.52 

898.88 

899.26 

899.63 

243 

900.00 

900.37 

900.71 

901.11 

901.48 

901.85 

902,22 

902.59 

902.96 

903.33 

244 

903.70 

904.07 

904.44 

901,81 

905.18 

905.55 

905,93 

906.30 

906.66 

907.04 

215 

907.41 

907.78 

908.15 

908.52 

908,88 

909,26 

909,63 

910.00 

910.37 

910.74 

246 

911.11 

911.48 

911.85 

912.22 

912.59 

912,96 

913,33 

913.70 

911.07 

914.44 

2l7 

914.81 

915.18 

915.55 

915,93 

916.30 

916.66 

i<17.01 

917.41 

917.78 

918  15 

218 

918.52 

918.88 

919.26 

919.63 

920.00 

920.37 

920.74 

921.11 

921.18 

921.85 

219 

922.22 

922.59 

922.96 

923.33 

923.70 

924,07 

924.44 

924.81 

9-25.18 

9-25.55 

250 

925.92 

926.30 

926.66 

927.04 

9:i7.41 

927.78 

928.15 

928.52 

9-28.88 

9-9.26 

251 

929.63 

930.00 

930.37 

930.74 

931.11 

931.48 

931.85 

932.22 

932.59 

932  96 

252 

933.33 

933.70 

931.07 

934.44 

931,81 

935.18 

935,55 

935.92 

936.30 

936.66 

253 

937.01 

937.11 

937.78 

938.15 

938,52 

938.88 

939.26 

939.63 

910  00 

940.37 

251 

940.71 

911.11 

941.48 

941.85 

912,22 

912.59 

912.96 

913.33 

913.70 

941.07 

255 

944.44 

944.81 

945.18 

945.55 

915,92 

916.30 

946,66 

947.04 

917.41 

917.78 

256 

918.15 

948.52 

948.88 

94d.26 

919.63 

95M.0O 

950,37 

950.74 

951.11 

951.48 

257 

951.85 

952.22 

952.59 

952.96 

953.33 

953.70 

951.07 

951.41 

9»1.81 

955.18  1 

258 

955.55 

955.92 

956.30 

956.66 

957,01 

957.41 

957,78 

958,15 

95S.52 

958.88  1 

259 

959.26 

959.63 

960.00 

960.37 

960,74 

961.11 

961,48 

961.85 

962.22 

962.59 

2fi0 

962.96 

963.33 

963.70 

964.07 

961.14 

964.81 

%5,18 

965.55 

965.92 

966.30  j 

261 

966.66 

967.04 

967.41 

967.78 

968.15 

968.52 

968.88 

969.26 

969.63 

970.00 

262 

970.37 

970.74 

971.11 

971.48 

971.85 

972.22 

972,59 

972,96 

973.33 

973.70 

I  263 

971,07 

971.44 

974.81 

975.18 

975.55 

975.92 

976.30 

976,66 

977.01 

977.41 

264 

977.78 

978.15 

978.52 

978.88 

979.26 

979.63 

980,00 

980,37 

980.71 

981.11 

265 

981.48 

981.85 

982.22 

982.59 

982.96 

98.i.33 

983,70 

981.07 

981.11 

981.81 

266 

985.18 

985.55 

9H5.92 

98t;.30 

986.66 

987.04 

987,41 

987.78 

988.15 

988.52 

1  267 

988.88 

989.26 

989.63 

990,00 

990.37 

990.74 

991.11 

991.48 

991.85 

992.22  J 

268 

992.59 

99^2.96 

993.33 

993,70 

991.07 

991.44 

994.81 

995.18 

995.55 

995.92 

269 

996.30 

996.66 

997.04 

997.11 

997.78 

998.15 

998,52 

998.88 

999.-26 

999.63 

270 

1000.00 

1000.37 

1000.74 

1001.11 

1001.48 

1001.85 

1002,22 

1002.59 

1002.96 

1003.33 

271 

1003.70 

1001.07 

1004.44 

1001.81 

1005.18 

1005.55 

1005,92 

1006.30 

1006.66 

1007.04 

272 

1007.11 

1007.78 

1008.15 

1008.52 

1008.88 

1009.26 

1009.63 

1010.00 

1010.37 

1010.74 

273 

1011.11 

1011.18 

1011.85 

1012.22 

1012.59 

1012.96 

1013.33 

1013.70 

1011.07 

1014.44 

274 

1011.81 

1015.18 

1015.55 

1015.92 

1016.30 

1016.66 

1017.01 

1017.41 

1017.78 

1018.15 

275 

1018.52 

1018.88 

1019.26 

1019.63 

1020.00 

1020.37 

1020.74 

1021.11 

1021.18 

10-21.85 

276 

1022.22 

1022.59 

1022.96 

10-23.33 

1023.70 

1024.07 

1021.14 

1024.81 

1025.18 

1025.55 

277 

1025.92 

1026.30 

1026  66 

1027.04 

1027.41 

1027.78 

1028.15 

1028.52 

10-28.88 

1029.-26 

278 

1029.63 

1030.00 

1030.37 

1030.74 

1031.11 

1031.48 

10.J1.85 

1032.22 

1032  59 

10S2  96 

279 

1033.33 

1033.70 

1034.07 

1031.44 

10-i4.81 

10a5.18 

1035..55 

10:J5.92 

10:J6  30 

1036.66 

280 

1037.01 

1037.41 

1037.78 

1038.15 

1038.52 

1038.88 

1039.26 

1039.63 

1010.00 

1010.37 

281 

1010.74 

1011.11 

1011.18 

1011.85 

1042.22 

1042.59 

10  2.96 

1043.33 

1043.70 

1044.07 

2-2 

1044.44 

1014.81 

1015.18 

1045..55 

1045.92 

1016.30 

1016.66 

1047.01 

1017.11 

1017.78 

283 

1048.15 

1018.52 

1018.88 

1019.V6 

1019.63 

1050.00 

1050.37 

1050.74 

1051.11 

1051.48 

284 

1051.85 

1052.22 

1052  59 

1052.96 

1053.33 

10.i3.70 

1054.07 

1054.44 

1051.81 

1055.18 

285 

1055.55 

1055.92 

1056.30 

1056.66 

1057.01 

1057.41 

1057.78 

105^.15 

1058.52 

1058.88 

286 

1059.26 

1059.63 

1060.(J0 

1060.37 

1060.74 

1061.11 

1061:48 

1061.85 

1062.22 

1062.59 

287 

1062.96 

1063.33 

1063.70 

1061.07 

1061.44 

! 064.81 

106.5.18 

1065.55 

1065.92 

1066.30 

288 

1066.66 

1067.01 

10.!7.41 

1067.78 

1068.15 

1068.52 

1068.K8 

1069.26 

1069.63 

1070  00 

289 

1070.37 

1070.71 

1071.11 

1071.18 

1071.85 

1072.22 

1072.59 

1072.96 

1073.33 

1073,70 

290 

1071.07 

1071.14 

1074  81 

107.5.18 

1075  55 

11175.92 

1076.30 

1076.66 

1077.04 

1077.11 

291 

1077.78 

1078.15 

1078.52 

1078,88 

1079.26 

1079.63 

1080.00 

1080.37 

108(1.74 

1081.11 

292 

1081.48 

1081.85 

1082.22 

1082.59 

1082.96 

1(I83..33 

1083.70 

1084.07 

1081.44 

1084.81 

293 

10S5.18 

1085.55 

1085.92 

1"86..S0 

1086.fi6 

1087.04 

1087.11 

1087.78 

1088.15 

1088.52 

291 

1088.88 

1089.26 

1089.63 

1090.00 

lii9tJ.37 

10  0.74 

lO'n.ll 

1091.48 

1091.85 

1092.22 

295 

1092.59 

10;12.96 

1093.33 

1093.70 

1091.07 

lfJ94.44 

1091.81 

1095.1S 

109.-..55 

1095,92 

296 

1096.30 

1096.66 

1097.(14 

1097.41 

1097.78 

1098.15 

1098.52 

1098.88 

1(J99  26 

1099.63 

297 

1100.00 

1100.37 

1100.74 

1101.11 

1101.48 

i: 01.85 

1102.22 

110259 

1102.96 

1103.33 

29  •! 

1103.70 

1104.' 7 

1104.44 

1101.81 

1105.18 

1105.55 

1105.92 

1106  30 

1106  66 

1107.04 

j  299   1107.11 

1107.78 

1108.15 

1108  52 

1108,88 

1109.26  '1109.63 

;  1110.00 

1110.37   1110.74 

43 


EXCAVATION   AND    EMBANKMEKT    TABLES. 


0.00    I  0.10    i    0.20  I  0.30  I    0.40 1  0.50    I  0.60    I  0.70  I  0.80  1 0.90 


300 

1111.11 

1111.48 

1111.85  i 

301 

1114.82 

1115.19 

1115.56  ? 

302 

1118.52 

1118.89 

1119.26 

303 

1122.22 

1122.59 

1122.96  : 

304 

1125.93 

1126.30 

1126.67  ! 

305 

1129.03 

1130.00 

1130.37  t 

30C 

113i.33 

1133.70 

1134.07 

307 

1137.04 

1137.41 

1137.78 

308 

1140.74 

1141.11 

1141.48 

30i> 

1144.44 

1144.82 

U45.19 

310 

1148.15 

1148.52 

1148.89 

311 

1151.85 

1152.22 

1152.59 

312 

1155.50 

ll.'>5  93 

1156.30 

313 

1159.26 

1159.63 

1160.(10 

314 

1162.96 

1163.33 

1163.70 

315 

1166.67 

1167.04 

1167.41 

316 

1170.  .7 

1170.74 

1171.11 

;ii7 

1174.07 

1174.44 

1174.82 

318 

1177.78 

1178.15 

1178.52 

319 

1181.48 

1181.86 

1182.22 

3-20 

1185.19 

1185.56 

1185.93 

321 

1188.89 

1189.26 

1189.{;3 

322 

1192.59 

1192.96 

1193.33 

323 

1196.30 

1196.67 

1197.04 

324 

1200.00 

1200.37 

1200.74 

325 

1203.70 

1204.07 

1204.44 

326 

1207.41 

1207.78 

1208.15  : 

327 

1211.11 

1211.48 

1211.85  1 

328 

1214.82 

1215.19 

1215.56  ' 

3-29 

1218.52 

1218.89 

1219.26  1 

330 

1222.22 

1222.59 

1222.96  1 

331 

1225.93 

1226.30 

1220.07  j 

332 

1229.03 

1230.00 

1230.37 

333 

1233.33 

1233.70 

1234.07 

334 

1237.04 

1237.41 

1237.78 

335 

1240.74 

1241.11 

1241.48 

336 

1244.44 

1244.82 

1245.19  i 

337 

124.S.15 

1248.52 

1248.89 

338 

1251.85 

12.-i2.22 

1252.59 

339 

1255.56 

1255.93 

1256.30  i 

340 

1-59.26 

1259.63 

1260.00 

341 

1262.96 

1263.33 

1263.70 

3t2 

1266.67 

1267.04 

1267.41  1 

34! 

1270.37 

1270.74 

1271.11  i 

314 

1274.07 

1274.44 

1274.82  i 

3i5 

1277.78 

1278.15 

1278.52  i 

346 

1281.4S 

1281.85 

1282.22  1 

347 

1285.19 

12S5.56 

l28.->.93 

348 

1288.89 

12«9.26 

1289.0 ! 

349 

1292.59 

1292.96 

1293.33 

350 

1296.30 

1296.67 

1297.04 

351 

1300.00 

1300.37 

1300.74 

35  i 

1303.70 

1304.07 

1304.44 

353 

1307.41 

1307.78 

1308.15 

354 

1311.11 

1311.48 

1311.85 

355 

1314.82 

1315.19 

1315.56 

356 

1318.52 

1318.89 

l:tl9.26 

357 

132J.22 

1322.59 

1322.96  1 

358 

1325.9:i 

1326.30 

1:120.67 

359 

1320.63 

1330.00 

1330.:J7 

1112.22 
1115.93 
1119.63 
1123.33 
1127.04 
1130.74 
1134.44 
1138.15 
1141.85 
1145.56 
1149..  6 
1152.96 
1156.67 
1160.37 
1164.07 
1167.78 
1171.48 
1175.19 
1178.89 
1182.59 
1186.30 
1190.00 
1193.70 
1197.41 
1201.11 
1204.82 
1208.52 
1212.22 
1215.93 
1219.63 
1223.33 
li27.04 
1230,74 
1234.44 
1238.15 
1241.85 
1245.56 
1249.26 
1252.96 
1256.67 
1260.37 
1204.07 
1207.7>* 
1271.48 
1275.19 
1278.89 
1282.59 
1286.!0 
1290.'  0 
1293.70 
1297.41 
1301. 1 1 
1304.'!2 
1308.52 
1312.22 
1315.93 
1319.03 
1323.33 
1327.04 
1330.74 


1112.59 
1110.30 
1120.00 
1123.70 
1127.41 
1131.11 
1134  82 
1138.52 
1142.22 
1145.93 
1149.63 
11.53.33 
11.57.14 
1160  74 
1164.44 
111-.8.15 
1171.85 
1175.56 
1179.26 
1182.96 
1186.67 
1190.37 
1194.07 
1197.78 
1201.48 
1205.19 
1208.89 
1212.59 
1216.30 
1220.00 
1223.70 
1227.41 
1231.11 
1234.82 
1238.52 
1242.22 
1245.93 
1249.03 
1253  33 
1257.04 
1260.74 
11264.44 
1268.15 
!  1271.85 
1275.56 
1279.26 
[1282  96 
11286.67 
1290.37 
1294.07 
129778 
11301.48 
11.305.19 
1308.89 
11312.59 
i  1316.30 
il '20.00 
11323.'?0 
1327.41 
1331.11 


1112.96 

1116.67 

1120.37 

1124.07 

1127.78 

1131.48 

1135  19 

1138.89 

1142.59 

1146  30 

1150  00 

11.53.70 

1157.41 

1161.11 

1164.82 

1168.52 

1172.22 

1175.93 

1179.63 

1183.33 

1187.04 

1190.74 

1194.44 

1198.15 

1201.85 

1205.56 

1209.20 

1212.90 

1216  07 

1220.37 

1224.07 

1227.78 

1231.48 

1235.19 

12  18.89 

1242  59 

1246.30 

1250.00 

1253.71) 

1257.41 

1261.11 

1264.82 

1268.52 

1272.22 

1275.93 

1279.6  i 

1283.33 

1287.04 

1290.71 

1294  44 

1298.15 

1301.85 

1305.56 

i:i09.26 

1312.96 

1316.67 

1320.:  7 

1324.07 

1327.78  I 

1331.48  I 


1113.33 

1117.04 
1120.74 
1124.44 
1128.15 
1131.85 
1135.56 
1139.26 
1142.96 
1146.67 
1150.37 
1154.07 
1157.78 
1161.48 
1105.19 
1108.89 
1172.59 
1176.  0 
1180.00 
1183.70 
1187.41 
1191.11 
1194-82 
1198.52 
1202.22 
1205.9:J 
1209.63 
1213.33 
1217.04 
1220.74 
1224.44 
1228  15 
12:11.85 
1235.56 
1239.26 
1242.96 
1240.67 
1250.37 
12.54.07 
12.57.73 
1261  48 
1265.19 
1268.89 
1272.59 
1276.30 
1280.110 
128  1.70 
1-/87.41 
1291.11 
1294.82 
1298.52 
1302.22 
1305.93 
1309.6;! 
l:n3.:« 
1317.04 
1320.74 
1324.44 
1328.15 
1331  85 


1113.70 
1117.41 
1121.11 
1124.82 
1128.52 
1132.22 
1135.93 
1139.63 
11143.33 
1147.04 
1150.74 
1154.44 
1158.15 
•1161.85 
1165.56 
1169.26 
: 1172.96 
1176.67 
1180.37 
1184.07 
1187.78 
1191.48 
[1195  19 
1198  89 
1202.59 
1200.30 
1210.00 
1213.70 
1217.41 
1221.11 
1224.81 
1228.52 
123222 
1235.93 
1239.6! 
1243  33 
1247.04 
1250.74 
1254.44 
1258.15 
1261.85 
1265.56 
1269.26 
1272.96 
1276.67 
1280.37 
1284.07 
1287.78 
1291.48 
1295  19 
1298  89 
1302.59 
1306.30 
1310.00 
1313.70 
1317.41 
1.321.11 
1324.81 
1328.52 
1332.22 


1114.07 
1117.78 
1121.48 
1125.19 
1128  89 
1132.59 
1136  30 
1140.00 
1143.70 
1147.41 
1151  11 
1154.82 
1158  52 
1102.22 
1105.93 
1109.03 
1173.33 
1177.04 
1180.74 
1184.44 
1188.15 
119185 
1195.50 
1199.26 
1202.90 
1200.07 
1210.37 
1214.07 
1217.78 
1221.48 
1225.18 
1228.^9 
1232.59 
1236.30 
1240.00 
1243.70 
1247.41 
1251.11 
1254.82 
1258,52 
1202  22 
1265.93 
1209.03 
1273.33 
1277.04 
1280.74 
1284.44 
1288.15 
1291.85 
1295.56 
1299.26 
1302  90 
1306  67 
1310  37 
1314  07 
1317.78 
1321.48 
1325.18 
1328.89 
1332.59 


1114.44 
1118.15 
1121.86 
1125.56 
1129.26 
1132.96 
1137.6? 
1140.37 
1144.07 
1147.78 
1151.48 
1155.19 
1158.89 
1162.59 
1166.30 
1170.00 
1173  70 
1177.41 
1181  11 
1184.82 
1188.52 
1192.22 
1195.93 
1199.63 
1203.33 
1207.04 
1210.74 
1214.44 
1218.16 
1221.86 
1225.55 
1229.26 
1232.96 
1236.67 
1240.37 
1244.07 
1247.78 
1251.48 
1255.19 
1258.89 
126259 
1266.30 
1270.00 
1273.70 
1277.41 
1281.11 
1284  82 
1288.52 
1292.22 
1295.93 
1299  63 
1303  33 
1307.04 
1310.74 
1314  44 
1318.15 
1321.86 
1325.55 
1329  26 
1332.96 


U  ENGINEER'S  FIELD  BOOK. 


Charles  S.  Ceoss,  the  author  of  the  preceding  pages,  was  graduated 
from  the  Rensselaer  Polytechnic  Institute  in  1838.  He  was  engaged  on 
railroad  location  and  construction  in  New  York  until  1852,  when  he  went 
to  Panama  to  report  on  the  railway  then  there  building.  Returning  in 
the  same  year,  he  was  mostly  employed  on  surveys  for  the  location  ol 
lighthouses  until  1857,  when  he  w<>nt  to  Minnesota  on  railroad  work.  It 
was  at  this  period  that  he  made  the  computations  for  the  tables  of  his 
pocketbook.  Later  he  had  an  extensive  practice  in  engineering  field 
work  in  New  York  and  New  England,  and  filled  many  responsible  posi- 
tions. He  was  a  man  of  great  integrity  of  character,  beloved  by  all  who 
knew  him.  He  died  in  Brooklyn  in  1880  or  1881.— Abstract  from  memoir 
of  his  life  in  Engineering  News,  May  8, 1886. 


A  good  engineer  must  be  of  inflexible  integrity,  sober,  truthful,  accu 
rate,  resolute,  discreet,  of  cool  and  sound  judgment,  must  have  command 
of  his  temper,  must  have  courage  to  resist  and  repel  attempts  at  intimi- 
dation, a  firmness  that  is  proof  against  solicitation,  flattery  or  improper 
bias  of  any  kind,  must  take  an  interest  in  his  work,  must  be  energetic, 
quick  to  decide,  prompt  to  act,  must  be  as  fair  and  impartial  as  a  judge 
on  the  bench,  must  have  experience  in  his  work  and  in  dealing  with  men, 
w  hich  implies  some  maturity  of  years,  must  have  business  habits  and 
knowledge  of  accounts.  Men  who  combine  these  qualities  are  not  to  be 
picked  up  every  day.  Still  they  can  be  found.  But  they  are  greatly  in 
demand,  and  when  found,  they  are  worth  their  price  ;  rather,  they  are 
beyond  price,  and  their  value  cannot  be  estimated  by  dollars. — Chief  En- 
gineer Starling's  Report  to  the  Miss.  Levee  Commissioners. 


CHAPTER  II. 


Engineering  Field  Work/ 


THE    SUKVEY8. 

The  three  classes  of  surveys,  viz :  Preliminary,  Location,  and 
Construction,  form  as  good  divisions  as  can  be  suggested  for  this 
subject,  and  we  will  consider  them  in  order. 

PBKLIMINARY. 

The  object  of  a  Preliminary  survey  is  to  ascertain  whether'it  be 
feasible  to  build  a  line  of  railway  between  two  points  upon  the  sur- 
face of  the  earth,  and  this  information  is  obtained  for  certain 
parties  \^ho  wish  to  make  money  in  some  way  or  other  by  con- 
structing or  having  such  line  of  railroad  constructed.  For  this 
purpose  the  parties  employ  a  more  or  less  competent  engineer  to 
make  these  surveys,  giving  him  authority  to  employ  one  or  more 
field  parties  according  to  the  magnitude  of  the  work,  and  the 
money  they  may  think  they  can  spend  upon  it.  If  only  one  party 
is  employed  it  is  sometimes  under  the  direction  of  the  chief  en- 
gineer himself,  but  more  commonly  under  an  assistant  employed 
by  him. 

ORGANIZATION    OF    FIELD    PARTY. 

The  organization  of  this  field  party  is  usually,  as  follows : 

1.  The  Assistant  in  charge  of  the  party. 

2.  The  Transitman,  whose  work  is  running  the  line  and  keeping 
all  notes  thereof. 

3.  The  Leveler,  whose  work  is  taking  levels,  drawing  the  profiles 
and  making  the  estimates  therefrom. 

4.  The  Level  rodman,  assistant  to  the  Leveler. 

5.  The  head  chainman,  who  should  also  carrv  the  transit  rod  and 
get  therewith  the  lines  given  by  the  transitman. 

6.  The  hind  chainman,  who  should  also  number  the  stakes  and 
keep. a  record  of  all  distances  measured. 

7.  From  one  to  five  axemen  according  to  the  amount  of  chop, 
ping  required  by  the  work. 

*  Written  by  the  Inte  Chas.  A.  Smith,  C.  E..  Professor  of  Civil  and  Mechanical 
Engineering  at  Washington  University,  St.  Louis,  and  published  in  Enqinkkb- 
iNO  News,  Vol.  III.  1876. 


46  ENGINEEKING  FIELD  WOKK. 

These  may  be  considered  about  all  the  men  needed  for  the 
professional  part  of  the  work,  and  if  the  country  is  inhabited  will 
be  all  that  will  be  employed ;  if  there  are  only  a  few  inhabitants  a 
team  and  driver  may  be  advantageous,  but  if  uninhabited  and  it 
becomes  necessary  to  take  a  camp  outfit,  at  least  two  more  men  are 
indispensable— a  teamster  and  a  cook,  the  latter  being  a  very  im- 
portant member  of  the  party. 

THE    ENGINEEK-IN-CHARaE. 

The  duties  of  the  engineer-in-charge  of  the  party  are  toe  many 
for  enumeration  here,  but  he  has  to  see  that  the  greatest  amount 
of  work  possible  is  done  for  the  money  expended  ;  his  business  is 
to  get  information  for  the  chief  engineer  and  to  keep  his  party 
running  without  delay.  A  word  of  brotherly  advice  to  him  may  not 
come  amiss  and  is  meant  kindly  if  it  is  not  necessary. 

CARE    OF    MEN. 

In  selecting  your  party  for  a  start  use  jufJgoroent  and  your  know- 
ledge of  human  nature;  don't  get  two  men  who  have  a  feud  with 
each  other  in  the  same  party  if  it  can  be  helped.  kStu;iy  your  men 
all  the  time  and  be  frank  and  free  with  them ;  do  not  talk  much 
with  them  in  working  hours,  but  warch  all  hands  very  closely,  for 
the  first  few  days  especially.  Kemember  that  your  men  are  men, 
and  treat  them  well:  show  them  that  you  know  how  the  work 
should  be  done,  but  don't  "nag"  them  all  ihe  time  ;  if  you  have  :». 
horse,  don't  keep  them  at  work  till  dark  and  then  ride  off  and 
leave  them  to  walk  three  or  four  miles  to  supper,  but  either  quit 
work  in  decent  season  or  lend  your  horse  to  some  fellow  who  is 
fagged,  and  walk  in  with  your  men ;  don't  hang  round  in  the  morn- 
ing and  let  your  men  wait  for  you,  but  pick  up  an  axe  or  rod  and 
start  first  for  the  work  ;  get  into  good  training  for  walking,  and  if 
you  start  for  supper  last  passall  the  men  on  the  road  ;  don't  shirk 
work  yourself,  and  don't  let  any  body  else  shirk;  never  ask  a  man 
to  do  any  work  you  would  not  be  willicg  to  do  yourself, — we  remem- 
ber "stripping  to  the  buff "  and  wading  a  stream  four  feet  deep 
when  the  cakes  of  ice  were  coming  down,  because  we  thought  the 
men  hung  back  and  did  not  want  to  go  into  the  water ;  don't  worry 
the  transitman's  wits  out  of  his  head  by  asking  him  questions ;  find 
out  what  he  is  doing  and  recording,  but  don't  crowd  him  too  hard 
or  bluster  about  him ;  don't  swear  habitually  before  the  men  if  you 


THE  COOK— ON  THE  LINE— THE  TRANSITMAN.  47 

can  help  it ;  you  may  want  to  swear  at  them  some  times,  and  if  not 
used  to  it  they  will  be  more  apt  to  obey;  don't  scold  a  man  when 
you  are  angry  yourself,  if  you  can  help  it,  but  wait  and  talk  to 
him  after  supper,  when  you  have  cooled  down. 

THE    COOK. 

In  selecting  a  camp  outfit  be  especially  careful  to  get  a  good 
cook,  and  we  advise  a  good  cooking  ptove  of  cast  iron  with  enough 
pipe  to  draw  well, — we  remember  a  sheet  iron  stove  which  had  to 
be  taken  down  every  morning  and  the  soot  kicked  out  of  it  before 
a  fire  could  be  made  to  "draw,"  and  we  also  remember  the  satis- 
faction with  which  the  boys  kicked  the  miserable  thing  to  pieces 
after  it  had  been  "returned"  at  headquarters.  We  are  more 
particular  in  this  matter,  not  only  because  we  like  to  be  well  fed, 
but  because  men  must  be  well  fed  in  order  to  work  well — and  you 
must  remember  that  poor  food  will  make  bad  temper  and  bad 
work,  and  that  the  interests  of  your  employers  demand  that  you 
keep  your  men  contented  with  their  job.  So  much  for  the  care  of 
the  men. 

ON    THE    LINE. 

Don't  let  your  leveler  get  too  far  behind  the  transit  work,  and 
see  that  he  checks  his  levels  and  establishes  benches  at  proper 
intervals.  After  the  work  is  well  started  you  will  be  obliged  to  go 
ahead  and  make  yourself  familiar  with  the  features  of  the  country 
and  select  the  points  where  your  line  must  be  run.  A  preliminary 
line  is  usually  run  without  curves,  and  the  work  of  the  transitman 
is  much  easier  than  in  location  surveys,  aod  the  line  work  is  much 
more  easily  carried  on  than  when  locating ;  and  this  brings  us  to 
the  work  of  the  transitman.  But  before  leaving  this  part  of  the 
subject  let  me  remind  you,  that  as  your  work  progresses,  you  will 
have  to  come  in  contact  with  the  property  holders  and  residents  of 
the  country,  and  you  should  always  bear  in  mind  that  you  repre- 
sent large  interests  and  can  give  them  by  your  manner  a  favoruble 
or  unfavorable  impression  as  you  choose. 

THE    TKANSITMAN. 

The  transitman  has  the  hardest  work  of  the  party  to  perform ; 
he  has  to  stand  with  one  eye  at  his  instrument  as  long  as  the  men 
can  set  stakes,  and  then  when  he  is  called  up,  the  whole  chain  and 
axe  force  have  to  be  idle  till  he  arrives  at  the  place  where  they  are 


48  ENGINEERING  FIELD  WORK. 

and  has  set  up  and  lined  his  instrument;  he  is  supposed  to  direct 
the  work  in  the  absence  of  his  superiors,  to  know  the  topography 
of  the  country  ahead  and  run  his  line  to  suit  the  ground— to  keep 
all  the  men  at  work  and  not  let  them  loaf  around — to  keep  all 
notes,  and  if  possible  sketch  all  the  topography;  to  act  as  chie 
assistant  in  every  way,  to  be  book-keeper  and  cashier  of  the  party ; 
if  in  camp,  to  purchase  supplies  and  see  that  things  go  right  gen- 
erally. The  skill  of  the  transitman  in  the  field  consists  in  his 
realization  of  the  peculiar  features  of  the  ground  and  his  judgment 
in  running  to  them,  and  to  his  being  able  to  work  under  mental 
pressure.  The  mere  instrumental  work  in  a  preliminary  survey  is 
easy  to  do,  as  it  consists  only  in  running  bearings,  noting  angles 
and  giving  the  line  to  the  men  at  the  chain.  A  few  words  to  the 
transitman:  Carry  your  instrument  yourself ;  don't  let  any  of  the 
men  take  it  at  night  unless  you  are  just  ready  to  drop  with  fatigue. 
Your  men  may  very  probably  ofifer  to  carry  your  instrument,  as  a 
common  courtesy,  or  even  to  make  friends  with  you,  but  don't 
accept  such  favors ;  among  working  men,  from  which  class  your 
chain  men  and  axemen  will  most  probably  come,  there  is  but  one 
standard  of  comparison,  and  that  is  strength,  and  although  one  of 
them  may  be  perfectly  willing  to  shoulder  j'our  fifteen  pound 
transit  for  three  or  four  miles,  you  will  not  gain  his  respect  by 
letting  him  do  it  for  you.  If  you  have  not  strength,  make  up  for  it 
in  endurance  and  quiet  pluck,  and  if  you  want  to  grumble,  don't  do 
it  before  the  men.  You  and  the  engineer-in-charge  must  be  in 
perfect  accord,  at  least  in  appearance,  if  you  want  to  further  the 
interests  of  your  employers  and  your  own  also.  In  setting  up  a 
transit  on  sideling  ground  it  is  generally  better  to  put  one  leg  of 
the  tripod  up  hill  and  two  down,  but  you  must  exercise  a  little 
common  sense  in  the  matter;  try  to  keep  the  lower  "parallel 
plate  "  as  level  as  possible,  as  by  so  doing  time  in  "  leveling  up  " 
will  be  saved ;  try  to  make  yourself  master  of  your  instrument  as 
there  is  a  great  range  in  the  value  of  transitmen,  and  try  to  "set 
up"  each  time  a  little  quicker  than  before,  and  also  a  little  better. 
The  acme  of  setting  a  transit  may  be  considered  reached  when  one 
shove  on  each  leg  of  the  tripod  brings  the  "plumb-bob"  exactly 
over  the  point  in  the  stake,  while  the  instrument  is  found  leve^ 
"both  ways.".  Try  and  see  how  many  times  you  can  do  this  every 
day,  but  don't  waste  time  studying  how  to  do  it  at  each  "  set."  It 
is  rather  better  to  keep  the  plates  clamped  together  at  zero,  and  do 
all  lining  of  the  instrument  with  the  lower  clamp  and  tangent; 


THE  LEVELEE^LEVELING.  49 

take  bearings  on  both  fore  and  back  sights  as  you  may  detect 
errors  in  reading  angles  by  so  doing,  and  be  careful  to  record 
which  way  angles  are  turned.  It  is  most  convenient  to  run  your 
transit  ahead  always  and  read  the  same  end  of  the  needle  if  the 
instrument  is  in  as  good  adjustment  as  it  should  be.  The  stability 
of  the  adjustment  differs  very  widely  in  different  instruments.  We 
have  worked  with  an  instrument  for  three  months  which  never  had 
to  be  touched,  and  also  with  another  from  the  same  maker  which 
would  not  reverse  truly  for  the  day,  although  adjusted  every 
morning ;  it  becomes  necessary,  therefore,  to  learn  the  peculiarities 
of  your  instrument,  and  know,  not  guess  at,  its  condition  at  all 
times.  The  reversal  should  be  tested  each  morning  before  going 
to  work  until  you  are  sure  of  the  instrument.  Learn  which  way  to 
get  the  slack  of  the  tangent  screws,  and  to  do  good  work  with  a  poor 
transit. 

THE    LKVELEB. 

The  leveler  on  a  preliminary  survey  may  have  to  work  at  his  best 
to  keep  up  with  the  transit  party,  and  as  the  leveler  and  rod  man 
have  to  work  completely  in  unison,  w.e  will  give  them  our  advice 
together  after  their  field  work.  Of  course,  in  the  office,  or  in  camp 
they  are  two  very  different  people,  the  leveler  being  one  of  the 
commissioned  officers  of  the  party,  if  we  may  use  a  military  term, 
while  the  rodman  is  about  the  grade  of  a  sergeant  only.  Still  there 
should  be  very  little  difference  of  feeling  between  them.  The 
leveler  keeps  all  field  notes  and  the  rodman  should  also  carry  a 
book  and  keep  the  turning  point  sights  and  work  out  all  heights  of 
the  instrument  and  elevations  of  turning  points  and  benches  in  t  e 
field.  Readings  for  turning  points  and  benches  may  be  ta  ken  to  the 
thousandths,  but  for  station  heights  the  nearest  tenth  only  should 
be  read. 

LEVELING. 

Make  all  the  vertical  height  you  can  in  going  up  or  down  hill 
as  you  may  save  a  setting  thereby.  Study  the  ground  as  to  what  is 
coming  ahead  and  never  select  turning  points  or  set  up  the  instru- 
ment without  having  fully  considered  what  is  to  be  done  next. 

Be  sure  of  the  adjustments  of  the  instrument  and  that  the  rod  is 
held  "plumb  "  (if  the  cross  hairs  are  right,  the  man  at  the  instru- 


bb  ENGINEERING  FIELD  WORK. 

ment  can  see  by  the  vertical  hair  if  the  rod  is  "plumb  "  one  way, 
and  by  gently  swinging  the  rod  in  the  plane  of  the  instrument  after 
setting  the  target  if  the  target  rises  above  the  hair,  the  rod  was 
not  held  "plumb;"  if  the  target  on  swinging  the  rod,  falls  below 
and  just  comes  up  to  the  hair,  the  rod  has  been  held  vertically). 
Make  your  signals  with  some  system,  and  move  the  rod  according 
to  the  signal  in  amount  of  motion  as  well  as  direction,  speak  your 
numbers  distinctly  and  don't  mistake  the  word  seven  for  eleven,  or 
the  reverse. 

Leveling  can  be  hurried  in  open  country  by  employing  two  rod- 
men  and  rods,  and  running  them  alternately,  the  employment  of 
a  fourth  man  to  keep  notes  in  such  case  being  a  great  help, 
although  such  great  haste  is  not  often  required  or  desirable. 

Put  in  benches  at  least  once  in  1,500  feet  in  open  country,  and 
every  1,000  feet  in  rough  country,  as  it  may  save  you  a  good  deal  of 
work ;  select  good  points  for  benches  and  turning  points,  and 
always  be  sure  that  the  instrument  may  be  moved  before  you  move 
it,' and  that  you  can  find  at  least  half  of  the  turning  points  in  the 
day's  work. 

In  running  "  check  levels  "  check  up  the  benches  every  mile,  and 
if  the  agreement  is  within  one-tenth,  call  bench  right  and  go  on. 
Try  to  keep  the  check  levels  within  two  miles  of  each  other,  as  it 
may  save  a  good  deal  of  annoyance. 

The  work  of  the  rest  of  the  party  is  much  the  same  for  location 
and  preliminary  surveys,  and  will  be  described  further  on.  The 
engineer  in  charge  of  the  party  and  the  transitman  are  the  ones 
whose  work  is  increased  the  most,  and  their  duties  will  be  described 
again  for  location  survey. 

THE    HEAD    CHAINMAN. 

The  head  chainman  holds  an  important  position  and  must  be  a 
man  with  sound  judgment,  and  must  understand  his  work.  He 
should  hold  the  transit  rod  with  one  hand,  and  the  chain  with  the 
other,  showing  discretion  as  to  holding  the  chain  level  and  taking 
short  lengths  on  hilly  ground  ;  he  should  understand  the  signals 
of  the  transitman  and  obey  them  intelligently ;  should  have  a  good 
eye  for  line  and  use  it  every  time  he  holds  his  rod  up,  so  as  to  be  as 
nearly  right  as  may  be  befor"^  the  transitman  begins  to  signal  to 
him ;  and  he  should  always  look  at  the  transitman  when  lining, 
instead  of  gazing  around  at  other  things.  His  work  is  perhaps  best 
conducted  in  the  following  order  •     When  the  chain  is  pulled  out 


HEAD  C&AINMAN-TRANSIT  POINTS.  51 

he  turns  around,  and  holding  the  rod  with  one  hand,  tries  to  place 
it  as  nearly  correct  as  he  can  by  lining  over  the  last  stake  to  the 
instrument,  while  with  the  other  hand  he  is  trying  to  "  straighten 
out  tlie  chain  ;"  he  then  moves  the  rod  in  obedience  to  the  motions 
of  the  man  at  the  instrument,  and  after  getting  the  line,  holds  the 
chain  up  to  the  rod  with  both  hands  and  gets  the  distance ;  then 
dropping  the  chain  he  stands  up  straight,  plumbs  the  rod  carefully 
and  receives  the  line  again  ;  then  pressing  the  rod  into  the  ground 
he  makes  the  hole  with  the  point,  and  takes  it  off  the  ground:  a 
stake  is  then  driven  and  the  measurement  should  be  repeated  to 
see  if  the  distance  is  correct,  after  which  the  rod  is  held  on  the  stake 
"  for  line,"  the  chain  is  then  dragged  on  and  the  operation  repeated. 
Time  may  be  lost  by  neglecting  the  order  of  operations  given  above, 
or  by  not  looking  to  see  where  the  line  is,  and  leaving  all  the  move- 
ments to  be  signalled  from  the  instrument,  or  by  jerking  the  chain 
while  trying  to  straighten  it,  or  by  not  watching  the  transitman 
closely,  and  thus  missing  his  signals.  If  you  are  so  far  away  that 
the  motion  cannot  be  seen,  take  your  handkerchief  or  hat  and 
make  a  signal  (imitating  the  lining  signals)  and  the  transitman  will 
understand  that  you  wish  him  to  take  his  handkerchief,  (when 
snow  is  on  the  ground,  his  hat)  to  increase  the  visibility  of  his  sig- 
nal. Eemember  that  the  transitman  can  see  you  plainly,  and  can 
guess  what  you  may  wish  him  to  do.  "When  you  wish  him  to  line 
you  hold  up  your  rod  and  wave  it  to  catch  his  eye,  and  when  you 
are  sure  that  the  line  can  go  no  further  without  a  change  in  the 
position  of  the  instrument,  you  must  call  his  attention  by  holding 
your  rod  in  both  hands  horizontally  above  your  head ;  then  after 
cai'efuUy  lining  and  centering,  you  can  call  him  up  by  beckoning 
with  both  hands,  holding  the  rod  above  your  head  or  by  any  other 
previously  arranged  signal. 

SELECTION    OF    TRANSIT    POINTS. 

By  far  the  most  important  duty  in  point  of  difficulty,  is  the  selec- 
tion of  the  transit  points,  which  must  be  so  chosen  that  the  greatest 
distance  ahead  may  be  seen  from  them  ;  in  general  they  should  be 
on  the  upper  edges  of  hills,  where  a  view  of  the  valley  on  both 
slopes  can  be  obtained,  and  if  possible,  where  a  full  view  of  the  tran- 
sit rod  can  be  had,  as  it  is  only  allowable  in  case  of  necessity  to 
sight  at  but  a  small  part  of  the  rod,  and  therefore  great  care  must 
be  taken  to  hold  "plumb"  at  all  times,  as  you  do  not  know  just 
how  much  of  the  rod  may  be  observed.    You  must  exercise  consid- 


52  ENGINEERING  FIELD  WORK. 

erable  judgment  in  the  matter,  and  never  be  astonished  if  youi 
views  and  the  transitman's  differ  on  this  point.  And  here  let  iis 
say  a  word  to  all  the  men ;  remember  that  the  transitman  has  to 
work  all  the  time,  and  that  he  has  to  take  all  the  blame  from  the 
engineer-in-charge  for  all  mistakes,  and  that"  if  he  does  scold  you 
for  things  that  are  not  your  fault,  just  wait  till  the  matter  devel- 
opes,  but  do  not  try  to  argue  during  working  hours  about  the  work : 
if  you  have  been  to  blame,  you  deserve  "jawing,"  and  if  you  have 
not,  it  will  not  hurt  you  a  bic  in  the  eyes  of  anybody  whose  opinion 
is  worth  having.  The  same  remarks  will  apply  to  the  transitmen 
and  levelers  in  their  relations  to  their  superior ;  let  them  remember 
that  the  engineer-in-charge  has  more  things  to  think  about  in  a  day 
than  they  have  in  a  week,  and  if  they  don't  believe  it,  wait  until 
they  have  the  same  position  and  can  see  for  themselves. 

THE    REAE    CHAINMAN. 

The  work  of  the  rear  chainman  is  to  hold  the  chain  while  it  is 
being  pulled  along ;  we  say  hold  it,  for  if  you  let  the  end  go  you  may 
have  to  call  the  front  chainman  back  for  10  or  20  feet  after  he  has 
passed  his  proper  distance,  and  he  won't  like  that.  Don't  hang 
on  the  chain  and  be  dragged  by  it,  but  be  ready  to  give  it  a  shake 
and  clear  it  if  it  catches  on  brush  or  rocks.  The  rear  chainman  is 
responsible  for  the  numbering  oi"  the  stakes,  and  for  all  distances 
with  "plus  "  numbers;  he  must  be  careful  to  assist  in  straighten- 
ing the  chain,  to  be  on  hand  promptly  in  measuring,  and  not  get  in 
the  line  nor  walk  on  the  line,  and  not  to  jerk  the  front  chainman 's 
arms  off  by  suddenly  stopping.  The  keeping  of  the  numbers  right 
is  a  more  difQcult  task  than  it  seems  to  be,  and  requires  a  good 
memory;  in  all  cases  of  doubt,  go  back  and  find  out  at  the  last 
stake  what  is  right  and  don't  guess  at  it.  Be  careful  that  the  chain 
is  in  good  order — that  the  links  are  straight  and  that  the  rings  are 
not  pulled  open.  Do  it  up  from  the  handle  and  keep  the  strap 
around  it ;  learn  to  throw  a  chain  over  a  stream ;  one  end  of  an 
ordinary  heavy  chain  can  be  thrown  over  a  50  feet  stream.  And  by 
making  two  bundles  with  say  15  feet  between  them,  and  using  two 
men  to  throw,  one  after  the  other  (at  say  half  a  second  interval),  we 
have  thrown  the  end  of  a  heavy  chain  75  feet.  Be  care!:ul  that  the 
chain  is  not  dragged  against  the  transit  legs,  and  do  not  hit  them 
while  trying  to  stand  the  straightening  as  inflicted  by  the  head 
chainman;  be  prompt  to  assist  in  making  short  chains  on  hilly 
ground,  and  on  curves,  if  there  are  any,  and  walk       the  outer  side 


AXEMEN— LOCATION— CARELESSNESS,  ETC.  53 

of  the  line  lest  you  get  in  the  "  line  "  of  the  instrument  without 
knowing  it. 

THE  AXEMEN. 

The  axemen  are  under  the  general  direction  of  the  head  chain- 
man  who  gives  the  line  for  cutting  brush  and  timber  with  his  rod. 
One  axeman  must  be  in  charge  of  the  stakes  and  must  never  let  the 
chain  work  wait  for  him  a  second,  but  must  keep  up  at  all  risk.  ( 
Sometimes  a  large  basket  is  useful  in  carrying  stakes.  The  stakes 
should  be  numbered  by  the  chainman,  and  if  he  marks  a  number 
of  them  in  the  basket,  care  must  be  taken  to  see  that  in  "plus  " 
stations  the  numbered  stakes  are  not  used,  or  the  numbers  may 
get "  mixed." 


In  location  surveys  the  only  difference  in  the  work  of  the  men  is 
in  the  curve  work,  where  the  head  chainman  has  to  offset  from 
the  line  of  the  last  stake  to  find  the  transit  "line  "  by  an  amount 
known  as  the  chord  "deflection,"  for  which  see  "Henck's  Field 
Bock."  We  always  gave  the  chainman  a  list  of  "chord  deflections  " 
for  the  even  degrees,  and  let  him  guess  at  the  amount  of  the 
ground,  and  found  that  it  saved  time.  The  centering  of  the  stakes 
should  be  attended  to  a  little  more  carefully  than  on  preliminary 
work,  and  the  measurements  made  with  more  care. 

A  back  rodman  will  be  necessary,  and  we  can  only  caution  him 
to  stand  up,  with  his  rod  in  position  all  the  time,  or  if  near  enough 
to  see,  whenever  the  transitman  turns  over  his  telescope,  he  must 
be  on  hand.  Although  the  job  is  not  very  intereeting  it  is  impor- 
tant. We  used  to  let  the  back  rodman  carry  the  coats,  and  if  we 
took  our  dinner  along,  a  basket  with  the  "grub." 

Each  man  in  the  party  must  be  held  strictly  responsible  for  what 
tools  or  instruments  are  put  into  his  hands,  and  a  careful  property 
account  must  be  kept  and  reported  from  time  to  time. 

WASTEFULNESS  OF  CABELESS  LOCATION. 

Location  surveys  diiTer  from  preliminary  surveys  in  being  more 
carefully  carried  out,  as  to  the  exact  position  of  the  line,  and  in  the 
curve  running,  which  is  usually  omitted  on  the  preliminary  work. 
The  exact  position  of  the  line  is  a  matter  of  great  importance,  for 
many  dollars  are  thrown  away  by  careless  locations  and  in  many 
cases  the  theory  of  wilful  ignorance  is  the  only  excuse  that  can  be 


54  ENGINEEEING    FIELD    WORK. 

• 

made  for  them.  There  are  needed  careful  judgment,  long  experi- 
ence, and  a  groat  deal  of  real  hard  work  on  the  part  of  the  engineer 
in  charge  of  the  locating  party,  to  make  successful  locations. 

THE  TOPOGEAPHER. 

The  party  is  usually  organized  with  the  same  force  as  in  the  pre- 
liminary  survey,  viz:  An  engineer-in-charge,  transitman,  leveler, 
level  rodman,  two  chainmen  and  from  one  to  five  axemen.  To 
these  are  often  added  a  toi)ographer,  and  sometimes  a  cross-section 
leveler  and  helper  or  rodman.  The  topographer  takes  sketch-notes 
of  the  contours  and  surrounding  country,  roads,  buildings  etc., 
which  have  to  be  shown  in  the  plans,  and  if  he  carries  a  pocket 
"  azimuth  compass,"  or  a  pocket  sextant,  he  will  find  it  a  great  help 
to  him,  but  for  his  work  we  esj^ecially  recommend  a  small  plane 
table,  18  inches  square,  with  the  paper  on  itin  "  block  "  fashion,  the 
board  fitted  with  a  shoulder  strap,  and  Jacob  staff  mountings,  and 
a  folding  "alidade  "  or  ruler,  with  sights.  With  this  outfit  a  topo- 
grapher can  produce  a  line  map  which  will  make  his  chief 
engineer's  heart  glad,  and  which  will  go  a  long  way  towards  con- 
vincing the  directors  that  the  party  have  done  a  lot  of  work.  Th«. 
use  of  the  plane  table  for  this  purpose  is  not  common,  but  sucb  ar. 
arrangement  costs  very  little,  and  nothing  else  will  show  as  much 
of  the  country  in  a  very  short  time.  The  field  use  of  the  instrument 
is  very  simple ;  the  line  already  run  being  platted  before  taking  the 
field,  the  "  orientation  "  can  be  performed  from  stakes  and  it  can  be 
used  anywhere. 

The  cross-section  leveling  is  only  performed  in  very  rough  coun- 
try; a  10-foot  pole  with  a  short  spirit  level  placed  on  it,  and  then 
held  wit 'a  one  end  on  the  ground  and  the  other  against  a  graduated 
rod  on  which  the  rise  or  fall  in  10  feet  is  noted,  is  used ;  the  infor- 
mation obtained  in  this  way  is  very  considerable :  there  is  a  good 
deal  of  work  to  get  it  but  the  men  are  not  reciuired  to  have  a  very 
high  grade  of  mental  organization  and  do  not  draw  a  very  high 
pay. 

ENGINEER  IN   CHARGE. 

All  of  the  increased  care  and  skill  required  and  already  men- 
tioned has  to  come  from  two  men— the  engineer-in-charge  and  the 
transitman— the  former  has  all  the  responsibility  of  the  added  im- 
portance of  the  survey,  and  the  constant  study  of  the  ever  changing 
ground,  and  the  greater  or  less  difficulty  of  the  work  itself:  nud 


ENGINEER  IN    CHAEGE-TRANSIT  NOTES.  55 

the  latter  has  all  the  curve  work,  with  increased  watchfulness 
and  greater  accuracy,  to  attend  to ;  those  two  men  have  their  work 
nearly  doubled,  while  the  work  of  the  rest  of  the  party  is  only  in- 
creased by  the  additional  care  and  attention  which  has  to  be 
enforced  on  ail  the  party. 

To  the  engineer-in-charg^  we  shall  say  very  little,  and  to  a  man 
in  that  position  little  can  be  said— if  he  does  not  know  his  business 
he  certainly  ought  not  to  be  in  the  place,  and  if  he  does  know  it, 
our  advice  is  unnecessary,  yet  if  he  does  not  think  it  beneath  him 
to  read  what  we  have  to  say  to  transitmen,  he  may  here  and  there 
find  a  hint  to  help  him  in  watching  the  work  of  that  indispensable 
assistant.  And  here  let  us  say  that  no  money  is  ever  sa  ed  by 
making  the  engineer-in-charge  of  the  location  run  either  transit 
or  level,  as  he  needs  all  of  his  faculties  to  be  at  all  times  shar- 
pened to  their  utmost  degree  to  attend  to  his  own  duties,  and  if  the 
tedious  instrumental  work  is  put  upon  him  he  cannot  keep  every- 
thing going  at  once  properly.  And  let  us  say  also,  that  if  the 
engineer-in-charge  wishes  to  make  every  man  do  his  very  utmost, 
that  he  had  better  take  the  head  of  the  chain  himself  when  he  can 
spare  tne  time,  especially  on  long  tangents,  which  he  has  already 
determined.  By  so  doing  he  will  be  near  all  the  men  of  the  transit 
party,  and  they  will  work  when  they  are  right  under  the  eye  of  the 
"  boss,"  and  he  will  be  sure  that  no  time  will  be  lost  in  picking  out 
the  transit  stations,  and  that  the  stakes  are  kept  well  up;  the 
transitman  will  always  hurry  up  to  him,  and  if  he  cannot  keep 
them  all  "  on  the  jump,"  he  is  not  fit  for  his  place.  Of  coui'se,  he 
has  frequently  to  go  ahead  and  pick  out  the  ground,  and  go  back 
to  see  how  the  profile  will  plat,  and  tell  the  transitman  what  must 
be  done  in  his  absence,  and  in  this  he  must  be  his  own  judge  of  his 
time  and  of  its  disposition,  but  still,  when  he  wishes  to  drive 
matters,  he  can  do  so  best  from  the  head  of  the  chain,  in  the 
meantime  letting  the  head  chainman  take  the  transit  rod  and  keep 
up  the  centers ;  the  mental  work  which  he  has  to  perform  all  the 
time  will  not  suffer  from  the  mere  manual  labor  of  being  head 
chainman. 

KEEPING  TRANSIT   NOTES. 

The  transitman  has  after  all  a  hard  place  to  fill,  for  there  is  no 
variety  in  his  mental  work ;  he  has  to  keep  a  sharp  watch  on  the 
men  when  his  superior  is  absent,  and  has  the  constant  computa- 
tion of  deflection  angles  to  attend  to  on  curves,  at  the  same  time 


66 


ENGINEERING    FIELD    WORK. 


using  all  possible  diligence  as  to  figures.  And  here  a  hint  as  to 
the  easiest  way  of  keeping  the  curve  notes  and  doing  the  transit 
work.  The  method  originated  we  know  not  how,  and  may  have 
have  been  used  by  large  numbers  of  transitmen,  although  we  have 
never  happened  to  meet  them. 

The  basis  of  all  circular  curve  work  with  the  transit  is  the  well 
known  theroem :  the  angle  between  a  tangent  chord,  or  between 
any  two  chords  which  meet  at  a  point  on  the  curve,  is  measured  by 
half  the  intercepted  arc.  And  as  the  point  where  the  chords  meet 
on  the  curve  may  be  anywhere  on  that  curve,  it  follows  that  the 
sum  of  any  consecutive  angles  or  series  of  angles  is  the  same  no 
matter  where  the  instrument  be  placed  on  the  curve  for  given 
arcs,  and  that  if  the  deflection  angles  be  all  computed  from  the  B. 
C,  as  far  as  may  be  desired,  at  any  station  on  the  curve  the  number 
can  be  used,  as  the  differences  will  be  the  same  for  the  same 
stations.    To  illustrate  this,  we  must  assume  an  example. 

Let  it  be  required  to  run  a  five  degree  curve  from  sta.  131  +  40, 
and  let  us  first  look  at  a  page  in  a  field  book : 


STATIONS. 

DEFLEC-  1 
TIONS. 

CURVE.    1 

TRUE  COURSE. 

NEEDLE 
COURSE. 

1'29 

N  161^  W 

N  16°  W 

130 

B.  C.  +40 

0-0' 

5°R. 

N  16=15'  W 

2 

1^30' 

3 

4-0' 

4 

6  30' 

5 

9=0' 

+50 

10O15' 

6 

II03O' 

7 

14^0' 

8 

16^30' 

E.  C.  +25 

17=7^ 

34-15' 

N  18-  0'  E 

N  17f 0  IE 

We  see  the  book  is  ruled  with  five  columns  and  usually  on  the 
left  hand  page,  the  right  hand  page  being  reserved  for  "  remarks." 
The  column  for  Stations  explains  itself,  the  signs  -'plus"  being 
used,  decimal  points  for  a  hundrea  foot  unit,  and  the  ordinary 
"  decimal "  being  reserved  for  feet  and  fractions  of  feet.  The 
letters  B.  C.  and  E.  C.  are  used  for  beginning  and  end  of  the  curve, 
instead  of  the  P.  C.  and  P.  T.  used  often  for  "  point  of  curve  "  and 
"point  of  tangent,"  being  more  in  accordance  with  the  usage  of 
ordinary  geometry  and   has   been   our  custom    for  several  years. 


KEEPING    TRANSIT    NOTES.  57 

The  column  of  deflections  contains  the  deflection  angles  com- 
puted from  B.  C.  as  far  as  convenient,  say  to  station  135,  ana  the 
stakes  set  and  centered,  for  same  reason  135  +  50  becomes  necessary  ' 
and  has  to  be  put  in ;  then  the  transit  is  turned  back  to  0^  and 
turned  over  on  the  back  sight  to  be  sure  that  nothing  has  slipped 
and  carried  up  to  135+50,  and  set  up.  The  instrument  is  then  set 
ii*-  0°  and  sighted  at  B.  C.  and  then  if  turned  to  10<^  15'  it  would  be 
on  the  tangent  at  135+50,  and  if  turned  to  11°  30',  it  will  be  on  the 
chord  from  135  +  50  to  136,  and  by  adding  these  2°  30'  for  each  hun- 
dred feet  the  curve  is  run  to  138  and  the  transit  is  moved  to 
that  place  after  taking  a  back  sight  as  before,  with  the  plates  at 
0°.  After  setting  up  at  138  if  we  could  see  B.  C.  we  should  set  at 
0°  again,  and  turning  to  16°  30'  we  would  be  on  the  tangent ;  but  B. 
C.  is  supposed  invisible,  and  we  shall  therefore  set  the  instrument 
at  10^  15'  and  sight  it  back  at  135  +  50  and  the  result  is  that  the 
lower  plate  is  in  the  same  position  as  if  B.  C.  had  been  visible,  and 
we  had  as  above  suggested  set  0°  and  sighted  thereat;  by  turning 
to  16°  30'  we  shall  be  on  the  tangent  at  130  and  if  we  find  that  1°  20' 
more  will  be  needed  to  strike  the  desired  direction  from  there,  we 
will  put  1°  15'  more  in  the  curve  or  37J'  deflection  which  corresponds 
to  25  feet ;  we  run  out  the  25  feet  and  turn  tolO^'  and  sight  the  stake 
in,  and  then  turning  to  10°15',  we  turn  over  to  the  back  sight;  af- 
ter satisfying  ourselves  that  it  is  all  right,  we  go  to  138  +  25  and 
being  sure  the  instrument  reads  10°15.  we  sight  again  at  135  +  50 
and  turn  to  17°7i'  and  are  at  the  tangent.  By  taking  the  differences 
and  comparing  distances  it  will  easily  be  seen  that  the  angles  are 
all  right. 

Now  in  what  does  this  method  consist  that  is  better  than  the 
practice  of  counting  stations  and  multiplying  by  the  deflection 
angle  ?  Only  this,  that  the  counting  and  multiplication  are  both 
performed  already.  Each  station  is  attached  to  the  angle  opposite 
to  it  in  the  note  book,  and  once  there  it  is  good  for  all  the  work 
that  you  can  do  with  it.  The  mental  labor  thus  saved  is  a 
great  help.  It  was  once  our  fortune  to  have  to  "break  in"  two 
"green"  transitmen  in  five  weeks,  and  in  all  that  time  we  com- 
puted every  angle  that  was  used  at  the  instrument,  mentally, 
and  kept  at  the  head  of  the  chain  most  of  the  time ;  by  asking 
the  man  at  the  instrument  what  reading  he  had  and  what  station 
he  was  at  and  what  his  back  rodman  was  at,  we  never  let  a  mistake 
pass  our  notice.  {Note. — We  are  not  anxious  to  repeat  this  experi- 
ence of  our  transit  running  from  the  head  of  the  chain.) 


58  ENGINEEBING    FIELD    WORK. 

For  the  transitman  himself  this  system  of  notes  is  a  great  relief 
as  he  is  free  from  the  constantly  recurring  question  "  what  is 
■your  next  deflection?"  with  its  importunate  worrying  when  he 
has  just  setup  on  an  odd  "plus"  and  knows  that  his  back  rod- 
man  is  also  on  an  odd  "plus,"  he  simply  asks  himself,  what  are 
the  readings  for  these  two  stations  knowing  that  the  difference 
l^etween  them  has  been  computed  carefully  once  as  they  come 
along,  and  it  will  be  all  right  now. 

COMPOUND  CURVES. 

On  compound  curves  the  same  method  can  be  followed  all  around, 
but  the  back  rodman  and  the  instrument  must  be  on  the  same 
branch  ( the  P.  C.  C,  point  of  compounding  of  curve,  is  of  course  on 
both  branches).  The  next  column  of  the  note  book  is  headed 
"  curves  "  and  in  it  are  recorded  the  degree  and  direction  of  the 
curves  and  the  central  angle, or  angle  of  intersection  ;  it  is  twice  the 
last  deflection  angle  always.  In  the  next  column  is  put  up  the  com- 
puted courses  from  the  first  one,  and  the  next  one  contains  the 
needle  readings;  the  use  of  these  is  a  check  to  the  transitmaq.'s 
work  and  sudden  variations  are  not  common.  If  "local  attraction  " 
exist,  it  can  be  found  by  reading  the  compass  at  each  end  of  the 
tangent.  We  remember  a  local  attraction  which  bothered  us  all 
one  morning  and  which  never  seemed  to  be  the  same  for  two  min- 
utes running,  and  which  quite  frightened  our  "  boss  "  but  as  we 
were  within  fifty  feet  of  a  north  and  south  track,  we  talked  "earth 
currents  "  at  him  (they  were  east  and  west )  and  as  we  were  sure  of 
our  work  we  let  it  go  unexplained  ;  in  the  afternoon  we  di.seovered 
.the  innocent  cause  to  be  a  small  "  Smith  &  Wesson  "  in  our  over- 
coat breast  pocket,  and  we  have  never  seen  any  such  local  attrac- 
tion since. 

LONG  TANGENTS. 

Long  straight  lines  require  a  good  deal  of  care,  and  the  instru- 
ment should  be  reversed  "  both  ways  "  on  them,  and  if  a  long  sight 
can  be  obtained  backward  so  as  to  overlook  two  or  three  transit 
points,  they  should  be  tested  by  the  direct  instrument.  If  great 
care  is  needed,  the  instrument  should  be  used  "both  wavs  "  without 
reversing,  and  the  slack  of  the  clamp  screws  watched.  Tangent 
screws  are  now  so  generally  made  double  that  the  play  of  the 
motion  screws  can  be  i>revented  from    interfering  with   the  ac- 


COMPOUND    CURVES-LONG    TANGENTS.  59 


curacy  of  the   work,   but  the  clamps   will  wear  loose  a  little  and 
must  be  watched. 

LAND    LINES. 

In  Railway  field  work,  after  the  location  survey,  follows  legi- 
timately the  land  surveyor  "land  lines"  as  they  are  called 
in  the  east,  and  although  most  of  this  work  is  included  in  com- 
mon surveying,  yet  there  are  some  points  of  difference  which  it  will 
be  well  to  touch  upon.  In  cities  and  towns  where  land  is  valuable, 
it  is  of  course  quite  important  to  have  the  work  done  accurately  ; 
and  although  in  the  western  country,  where  the  land  is  very  com- 
monly given  to  the  railroad  company  it  is  not  so  essential,  still  it  is 
always  desirable  to  know  how  to  do  good  work,  and  a  few  words  as 
to  general  surveying  will  scarcely  be  out  of  place. 

In  the  first  place  be  sure  that  your  work  is  definitely  connected 
with  points  which  can  be  found  again,  and  that  the  connection  with 
the  main  line  is  right,  and  that  it  is  simple ;  any  complex  mea- 
surement is  to  be  avoided.  In  the  next  place,  measure  every  dis- 
tance pertinent  to  the  work  which  can  l>e  directly  measured.  Cal- 
culate as  little  as  possible.  If  the  land  to  be  taken  is  very  irregular 
in  form,  a  "  traverse  "  is  the  best  method  of  attack  if  all  the  sides 
can  be  measured;  don't  have  any  "  omissions "  to  supply  if  you 
can  help  it ;  be  careful  to  take  all  offsets  at  right  angles ;  take  the 
angles  with  a  transit  if  one  can  be  had,  and  donot  use  the  com- 
pass in  any  way  but  as  a  check  on  the  transit ;  for  sighting  right 
angles  quickly,  some  of  the  forms  of  the  "  optical  square  "  may  be 
found  very  convenient;  for  ordinary  work  in  cities  most  of  the 
measurements  for  land  will  be  at  right  angles  or  nearly  so,  and 
the  woi'k  oan  be  laid  out  on  four  lines  forming  a  trapezium ;  do  not- 
trust  to  any  building  for  a  right  angle  or  to  any  two  walls  of  the 
same  building  to  have  parallel  faces ;  brick  laying  is  not  by  any 
means  the  most  exact  of  trades,  and  although  for  a  map  the  errors 
will  not  show,  yet  for  other  work  to  be  connected  to  that  in  progress. 
it  may  lead  to  serious  errors. 

For  railroad  purposes  the  land  is  usually  found  in  long  narrow 
strips  of  varying  width ;  and  it  is  sufficient  to  find  the  length  on  the 
centre  line,  and  directions  of  bounding  lines  which  cross ;  it  is 
however,  desirable  to  have  all  "land  lines"  within  four  or  five 
hundred  feet  of  the  track,  and  this  requires  measurements  on  the 
crossing  lines.    In  getting  the  direction  of  a  fence,  when  the  instru- 


60  ENGINEEBING    FIELD    WORK. 

ment  is  placed  at  one  side,  measure  the  distance  from  the  instru- 
ment to  the  fence  at  right  angles  to  it  and  have  a  similar  "  offset " 
made  as  far  as  possible  from  the  instrument ;  of  course  the  main 
iine  should  have  been  run  and  the  transit  placed  in  the  line  before 
the  direction  can  be  obtained. 

For  street  surveying  the  best  method  is  that  of  a  line  in  the  mid- 
dle, with  offsets  and  measurements  connecting,  the  offsets  at  the 
end  as  well  as  the  line  run.  In  very  crowded  streets  we  have  some- 
times run  a  line  down  each  footwalk,  connected  them  carefully  at- 
their  ends,  and  then  proceeded  as  described  for  a  single  line. 

CAREFUL   NOTES 

In  all  work  of  this  kind  the  most  important  thing  is  to  take  good 
notes ;  always  put  these  down  as  if  you  expected  to  die  before 
morning,  and  wanted  to  leave  them  in  such  good  condition  that  in 
ten  years  time  a  stranger  with  no  previous  acquaintance,  and  with  no 
one  of  the  old  party  to  help  him,  could  take  your  book  and  proceed 
on  the  job  without  delay ;  if  this  can  be  done,  your  notes  must  be 
about  right,  but  you  never  will  have  them  too  complete.  We  have 
never  used  any  but  the  "sketch  system  "  for  taking  notes,  and  we 
always  made  them  in  the  field,  and  copied  them  over  on  the  next 
page  in  ink,  thus  keeping  the  rough  set  with  the  original  figures, 
and  the  finished  set  to  explain  them ;  the  original  figures  have 
more  weight  as  evidence,  but  the  explanation  given  by  a  neat  ink 
copy  is  a  very  great  help  in  interpreting  them.  For  city  work  take 
all  angles  with  the  transit  more  than  once,  that  is  to  say,  "repeat 
them,"  three  or  four  times  which  is  enough  ;  the  object  of  the  "  re- 
peating "  being  to  check  the  angle  and  not  to  subdivide  the  vernier 
reading, 

PBESEEVING  THE  LINES 

After  the  completion  of  the  land  survey  comes  the  actual  field 
work  preparatory  to  the  construction,  and  here  it  is  customary  to 
reduce  the  number  of  men  in  the  party  and  to  begin  to  "  cut  down 
expenses  "  in  the  engineering  department. 

The  first  thing  to  be  done  is  to  "  preserve  "  the  line,  that  is,  to  con- 
nect all  tangent  points  with  stakes  that  are  away  from  the  line  and 
far  enough  from  it  not  to  be  disturbed  by  the  operations  of  grading" 
and  earthwork ;  at  the  same  time  the  slope  stakes  should  be  set  and 
marked  with  the  cut  and  fill — also  the  cut  or  fill  should  be  marked 
on  the  centre  stakes— this  work  can  all  be  done  on  the  same  job,  and 


CENTEES  AND  GRADES-QUALIFICATION.  ETC.       61 

thus  the  contractors  can  make  a  start  at  once  if  they  so  wish ;  of 
course  a  record  of  all  tield  work  is  required,  and  the  results  should 
all  be  put  in  the  grade  book.  For  setting  slope  stakes  the  only  sat- 
isfactory method  is  with  the  Leveling  instrument,  though  for  com- 
paratively smooth  ground  and  light  work,  there  are  various  devices 
for  setting  slopes  which  involve  much  less  work,  and  are  sufiQciently 
accurate  for  use. 

CENTRES  AND  GRADES. 

Most  of  the  work  for  railroads  in  construction  consists  in  setting 
"  centres  "  and  "  grades ;"  for  the  former,  in  nine  cases  out  of  ten, 
the  line  can  be  run  in  without  an  instrument,  if  the  known  points  are 
convenient ;  the  Tangent  Deflections  are  useful  for  running  curves 
with  only  the  chain  and  rods  for  lining ;  for  approximation  there  is 
a  very  convenient  method  of  computing  angles  and  distances 
(measured  as  arcs)  which  it  is  well  to  be  familiar  with  in  the  absence 
of  all  **  pocket-books."  At  one  hundred  feet  distance  three-hun- 
dredths  of  one  foot  subtends  one  minute  of  arc.  Strictly  speaking  it 
is  twenty-nine  one  thousandths  instead  of  three  one  hundredths.  At 
the  same  distance  one  foot  and  three-quarters  subtends  one  degree 
of  arc,  but  one  and  eight-tenths  can  generally  be  used.  With  this 
once  fixed  tirmly  in  the  mind,  mental  computations  can  be  made 
with  the  greatest  ease.  As  an  example  of  this  let  it  be  required  to 
find  Tangent  and  Chord  Deflection  for  100  feet  chord,  and  for  60  feet 
chord,  and  ordinate  at  centre  of  100  feet  chord  for  a  5°  curve  :  5X1.8 
=9.00°  for  the  Chord  Deflection,  and  4  5'  for  the  Tangent  Deflection 
100  feet  chord:  4.5X0.6=2.7'— 2.7X0.6.=1. 62  Tangent  Deflection  for 
the  60  feet  chord,  and  \  of  the  Tangent  Deflection  for  100  feet  chord 
=11'  for  the  middle  ordinate.  These  values  are  all  in  excess,  and  if 
the  deflections  are  to  be  used  for  running  the  curve  more  than  one 
station,  the  value  1|'X5=8|'  should  be  used,  and  this  is  in  error  only 
about  f  of  an  inch.  A  great  many  other  computations  may  be  thus 
performed  mentally,  and  the  work  already  done  checked  by  these 
approximations,  and  the  real  blunders  found. 

QUALIFICATIONS  FOR  LEADER. 

There  are  many  ways  of  doing  most  kinds  of  field  work,  and 
many  methods  are  described  in  the  books  under  various  heads— but 
a  good  knowledge  of  geometry  and  trigonometry,  and  possibly  a 
little  familiarity  with  analytic  geometry,  combined  with  a  cool 
head,  and  an  appreciation  of  the  external  circumstances,  will  en- 


62  ENGINEERING    FIELD    WORK. 

able  a  man,  after  a  limited  experience,  to  become  competent  to 
take  charge  of  a  party  in  the  field,  as  far  as  the  mere  theory  of  the 
operations  is  concerned — but  a  knowledge  of  human  nature  and 
sound  judgment  are  required  to  give  satisfactory  results. 

CULVERTS  AND   MASONBY. 

We  would  say  a  word  about  the  staking  out  of  culverts  and 
masonry,  and  will  begin  with  a  hint  about  box  culverts.  On  ma- 
sonry of  this  class  it  is  well  to  put  in  four  stakes  on  the  lines  of 
tlie  face  of  each  wall,  one  at  each  end  of  each  line,  and  two 
stakes,  one  on  each  end  of  a  line  terminating  the  culvert  at  the 
proper  distance  out,  found  as  in  slope  stakes.  These  stakes 
must  all  be  placed  outside  of  the  trenches,  and  should  be  at  such  a 
distance  from  the  work  that  they  will  be  safe  during  the  construc- 
tion. 

BBIDGE  ABUTMENTS. 

Bridge  abutments  on  shore  can  be  given  in  the  same  way,  and  if 
in  the  water  by  parallel  lines,  or  sighting  frames  made  out  of  strips 
of  wood.  Piers  can  be  located  by  sights  on  shore,  or  as  they  are 
commonly  termed  "ranges." 

EARTHWOBK  MEA8UBEMENT. 

If  earthwork  is  to  be  measured  in  a  "borrow pit,"  the  best 
way  is  to  run  out  two  sets  of  lines  at  right  angles  over  the 
ground,  denoting  distances  in  one  direction  by  letters,  and 
in  the  other  direction  by  numbers,  and  taking  the  levels  all 
over  the  ground  denoting  the  stake  by  both  letter  and  number,  and 
then  every  month  as  the  work  is  done,  these  stakes  can  be  replaced 
and  the  levels  taken  again.  The  bounding  lines  of  this  system 
should  be  carefully  put  in,  and  the  stakes  may  have  permanent 
"  sights  "  put  up  over  them  ;  in  this  case  the  stakes  of  the  system 
can  be  replaced  without  a  transit.  Of  course  the  bounding  lines 
should  be  wholly  outside  the  work  and  there  can  be  little  trouble 
in  taking  care  of  the  work  in  this  way. 

RETAINING  WALLS. 

Retaining  walls  are  very  usually  set  out  by  stakes,  but  "  sighting 
frames"  outside  the  wall  and  inline  with  it  are  to  be  prepared, 
if  the  height  is  not  too  great. 


TUNNELS— EESPONSIBILITY  OF  AN  ENGINEER.       63 


TUNNELS. 

Underground  work  in  tunnels  is  usually  kept  in  line  and  grade 
by  points  ou  the  roof;  their  stability  and  permanence  are  much 
greater  than  if  given  on  the  bottom  of  the  tunnel.  In  rook  work 
where  stakes  can  not  be  used,  chisel  marks  are  made  to  serve  as 
points.  Such  work  requires  less  frequent  attention,  but  is  more 
important, 

RESPONSIBILITY  OF  ENGINEER. 

And  now  in  closing,  let  us  add  a  word  as  to  the  responsibility 
resting  upon  the  engineer  when  setting  out  work. 

Few  beginners  appreciate  the  necessity  for  correct  work,  and  do 
not  realize  that  a  blunder  undetected  may  cause  a  loss  to  the  con- 
tractor of  a  great  deal  of  money,  and  that  if  he,  as  the  company's 
authorized  agent,  makes  a  mistake  in  his  work,  the  company  may 
become  liable  for  many  times  his  salary,  and  that  his  discharge  is 
a  very  small  amelioration  of  matters  which  he  has  mixed.  Pecuni- 
ary responsibility  must  be  fully  appreciated  in  order  to  have 
accurate  work  done. 

Mistakes  in  woi;k  are  not  only  discreditable  but  they  are  dishon- 
orable, and  to  the  feelings  of  the  suffering  party  they  seem  crimi- 
nal. Now  as  man  is  liable  to  error,  work  must  always  be  in  some 
way  checked,  and  a  mistake  which  is  discovered  by  the  maker  in- 
time  to  be  rectified  by  him  before  any  damage  is  done  is  in  no 
way  discreditable,  provided  however  that  it  does  not  happen  too 
often,  and  that  the  same  class  of  mistake  is  not  made  the  second 
time.  Nothing  gives  a  contractor  less  respect  for  the  engineer 
than  finding  his  mistakes,  even  if  they  have  caused  no  damag"^. 


ENGINEERING  FIELD  WORK. 


STAKING  OUT. 


"What  is  that,  mother?" 

'The  Rodman,  my  chUd. 
His  footsteps  are  weary,  his  accents  are  wild; 
His  hair,  how  disordered!  his  eyeballs,  how  blearl 
And  see  where  his  necktie  hangs  under  his  ear." 
"Rod  up  there!    Hold  her  steady!  !    Go  on  down  the  hill  I  1 1 
7.8.    Cut  2.3— No,  begosh  it's  a  fill. 
Half  the  roadbed;  13  +  the  slope  1.1; 
No,  it's  H  though,  as  sure  as  a  gun. 
Well,  that  makes— let's  see — O!  stick  her  in  there. 
It'll  do.     Perhaps  the  contractor  will  swear. 
But  no  difference:    We're  the  big  dog  in  this  fight. 
No  matter  what's  wrong,  just  swear  it's  all  right. 
A  contractor  don't  know  a  beefsteak  from  a  bone. 
Now  pick  up  your  tools,  and  let's  pull  out  for  home." 
J.  H.  K.  B., 

Laurel  Hill  Swamp  Angel. 
—From  the  S.  P.  R.  R.  Transit. 


CHAPTER  III. 


REGULATIONS   FOR   THE 

Engineering     Department 


DURING 


CONSTRUCTION.* 


BY  WM.  F.  SHUNK,  C.  E. 


I.   ORGANIZATION. 


1.  The  chief  engineer  will   have  exclusive  control  of  this  department. 

3.  He  may  be  aided  by  a  consulting  engineer,  without  executive  pow- 
ers, and  an  associate  engineer,  acting  under  his  immediate  direction,  to 
whom  all  official  communications  from  subordinates  should  be  addressed, 
and  whose  orders  concerning  the  work,  or  matters  thereto  appertaining, 
shall  be  received  as  authoritative. 

3.  The  associate  engineer  shall  be  aided  by  such  a  staff  of  division  en- 
gineers, principal  assistant  engineers,  draughtsmen,  clerks,  and  other 
helpers  as  shall  be  approved  by  the  cliief  engineer. 

4.  Each  division  engineer  shall  have  charge  of  the  construction  of  about 
thirty  miles  of  road,  in  sections  approximating  one  mile  long  and  subdi- 
visions composed  of  from  six  to  ten  sections. 

5.  Principal  assistant  engineers  may  be  appointed  to  special  charges, 
such  as  important  structures,  the  compilation  of  records,  the  preparation 
of  plans  and  the  like.  Where  such  charges  fall  within  the  tenitorial 
limits  of  a  division  engineer,  strict  definition  of  responsibility  will  be  made 
and  hearty  co-operation  expected. 

*  South  Pennsylvafiia  R.R. 


66  ORGANIZATION-PREPARATORY  WORK. 

6.  Division  engineers  shall  have  power  to  employ  one  draughtsman  for 
the  division  headquarters  office,  and  such  resident  engineer,  inspectors, 
time  keepers,  and  other  helpers  on  the  line  of  road  as  may  be  necessary 
for  the  proper  conduct  of  the  work  for  which  they  are  immediately  re- 
sponsible, subject  beforehand  to  the  approval  of  the  associate  engineer  ; 
and  to  suspend  or  discharge  such  employes  for  sufficient  causew  The 
power  of  removal  should  be  exercised  discreetly,  and  seldom  without 
reference  to  the  associate  engineer. 

7.  Each  resident  engineer  shall  be  aided  by  one  rodman,  competent  to 
use  transit  and  level,  two  tapemen,  and  one  axeman,  until  the  hne  is  cross 
sectioned.  Thereafter  one  tapeman  may  be  dispensed  with.  Special  as- 
signments of  force  will  be  made,  when  necessary,  to  divisions  which  in- 
clude large  tunnels.  Each  resident  engineer  shall  have  power  to  appoint, 
suspend  or  remove  his  own  subordinates,  subject  to  the  approval  of  the 
division  engineer. 

8.  Good  discipline  and  orderly  management  require  that  all  official 
commimications,  verbal  or  written,  shall  pass  from  the  superior  to  liLs  im- 
mediate subordinate,  or  from  the  subordinate  to  his  immediate  superior. 
Should  any  emergency  necessitate  a  deviation  from  this  rule,  the  party 
intermediately  concerned  should  be  informed  of  it. 


n.  PREPARATORY  W'ORK. 

1.  First  of  all,  division  engineers  shall  cause  the  centre  line  of  location 
on  their  respective  divisions  to  be  accurately  retraced,  established  and 
test  leveled. 

2.  This  done,  they  shall  furnish  promptly  to  the  associate  engineer  a 
map  in  duplicate  of  their  respective  divisions,  scale  four  hundred  feet  to 
an  inch,  one  copy  to  be  on  mounted  drawing  paper,  the  other  on  tracing 
linen,  showing  the  centre  line  and  proposed  right-of-way  boundaries  in  red; 
intersected  and  adjacent  property  lines  with  names  of  owners,  political 
boundaries,  contours,  streams,  roads,  woodland,  buildings,  and  other  ob- 
jects proper  to  a  working  map,  in  black;  also  a  profile,  similarly  duplica- 
ted, to  "Plate  A"  scale,  upon  which  shall  be  marked  the  estimated  quan- 
tities in  each  cut  and  fill,  the  character  of  the  material,  the  alignment 
corresponding  to  map,  and  the  proposed  grade  line,  the  latter  to  be  pen- 
ciled on  the  paper  duplicate  and  drawn  very  finely  on  the  tracing  in  red, 
with  its  rates  per  centum  and  elevations  of  change  points  clearly  figured. 

3.  The  paper  copy  of  each  of  said  duplicates  will  be  returned,  with 


PREPARATORY  WORK. 


67 


such  alterations  as  the  chief  engineer  may  think  proper  to  make  or 
approve,  and  endorsed  with  his  approval,  or  that  of  his  associate,  to  the 
division  engineer,  who  shall  place  them  on  file  in  his  office. 

4.  Thereafter  no  change  of  line  or  grade  wUl  be  permitted,  excepting 
upon  compUance  with  the  like  form  of  procedure,  namely:  The  submis- 
sion of  duphcate  drawings  of  the  change  proposed,  and  the  return  of 
copies  approved  by  the  chief  engineer  or  his  associate. 

5.  Division  engineers  shall  cause  to  be  prepared  for  each  of  their 
Residents  copies,  from  the  foregoing  approved  map  and  profile,  of  the 
respective  subdivisions,  and  also  a  pencil  record  of  location,  in  the  fol- 
lowing form,  to  be  called  the  ''Location  Record,  Div.  No.  .  .  Subdiv.^ 
No.     .     : 


6.  In  the  station  column,  transit  points  should  be  marked  with  a  circle, 
as  usual,  and  tu^rning  points  inclosed  with  a  triangle  in  addition  to  the 
circle.  Directly  below  every  turning  point  record  the  note  should  be 
made,  "B.  S.  to  .  .  .  ."  indicating  the  backsight  point;  and  in  the 
deflection  column  should  be  recorded  the  total  deflection,  at  each  turning 
point,  from  the  range  of  backsight  to  that  of  foresight.  By  means  of 
such  a  record  the  line  can  in  future  be  retraced,  not  only  over  the  same 
points,  but,  failing  one  or  more  of  them,  with  the  same  angles  used  on 
the  establishment  of  location. 

7.  The  alignment  column  must  show  the  calculated  course  and  the 
length  of  each  tangent,  thus;  N.  64°  35'.  W. — 3,972  feet;  and  the  degree, 
length,  angle,  and  apex  distance  of  each  curve,  thus:  5'  C.  R.  (or  L.)— 
650  ft.;  angle,  32^  30';  A.  D.  334  feet. 

8.  The  colmnn  of  remarks  should  contain  notes  of  benches,  land, 
stream,  timber,  and  road  lines,  and  other  matters  of  interest  relating  to 
the  line  or  the  work  to  be  constructed.  The  cross-section  columns 
fchould  be  reserved.  Stations  should  be  entered  on  every  third  line  of  the 
book  only,  thereby  recording  about  eight  hundred  feet  per  page,  to  pro- 
vide for  subsequent  additions. 

9.  The  original  book  from  which  the  copies  are  made,  should  be  re- 
tained by  the  division  engineer.    . 


RIGHT  OF  WAY. 


ni.   EIGHT  OF  WAY. 


1.  Division  engineers  sliall  next  cause  the  necessary  surveys  for 
right-of-way  to  be  made,  and  maps  thereof  to  be  prepared  on  "Topo- 
graphy" paper,  scale  two  himdred  feet  to  an  inch,  shpwing  the  plan  of 
land  to  be  taken,  the  contents  of  severalties  in  acres  and  hundredths,  the 
Township,  Covinty  and  State  wherein  situated,  owners'  names,  road 
crossings,  streams,  buildings,  woodland,  meridian  line,  and  other  objects 
needful  or  useful  in  such  an  exhibit. 

2.  These  maps  shall  be  consecutively  numbered,  and  shall  have  a 
blank  margin  two  inches  wide  on  the  left  edge,  that  they  may  be  bound 
in  volumes  for  the  Company's  archives.  When  more  than  one  property 
is  represented  on  a  sheet,  the  severalties  shall  be  designated  by  the  sheet 
number  and  an  annex  letter,  "a,"  "6,"  etc. 

3.  Division  engineers  shall  furnish  to  the  land  agent  appointed  by 
the  Company,  when  requested  by  him,  a  tracing  from  these  maps  num- 
bered and  sub-lettered  to  correspond  with  the  original,  together  with  a 
description  of  each  property,  for  incorporation  with  the  deeds. 

4.  Currently  with  the  purchase  of  right-of-way,  or  as  soon 
thereafter  as  more  important  service  shall  permit,  division  en- 
gineers shall  cause  the  boundaries  of  the  Company's  property  to 
be  marked  by  corner  and  line  stones,  or  other  endurable  monuments. 
This  should  be  done  before  ground  is  broken,  if  possible,  and  said  monu- 
ments should  be  carefully  maintained  during  the  progress  of  construction. 

5.  Division  engineers,  in  laying  out  proposed  land  purchases  on  the 
maps,  prescribed  in  (II.,  3,)  should  provide  amply  for  station  grounds 
extra  tracks,  borrow  pits,  and  spoil  banks,  and  call  attention  thereto  by 
explanatory  notes  on  said  maps. 

6.  The  lay-out  shaU  be  for  a  double-track  railroad,  tracks  thirteen 
feet  between  centres.  Sixty  feet  shall  be  the  minimum  width  taken 
in  any  case,  without  the  express  approval  of  the  chief  engineer  or 
his  associate ;  and  as  a  general  rule,  a  berm  twelve  feet  wide  on  each 
side  of  the  road  formation  shall  be  included  in  the  Company's  right- 
of-way. 

7.  The  Company's  boundary  line  shall  generally  be  parallel  to  the 
centre  line  of  the  railroad,  and  right-of-way  widths  shall  change  by  jogs 
square  to  said  centre  line,  excepting  at  the  bounds  of  severalties,  where 
changes  of  width  should  be  located,  whenever  convenient,  and  conform- 
ably to  existing  land  lines. 


FINAL  PREPARATIONS  FOR  CONSTRUCTION.  69 

IV.  FINAL  PREPAEATIONS  FOR  CONSTEUCTIOX. 

1.  The  centre  line  having  been  established  and  test-leveled,  agreeably 
to(n.,l,)it  should  now  be  gone  over  with  the  level  very  carefully, 
setting  stakes  at  "grade"  points  and  at  changes  of  sm-face  necessitating 
additional  cross-sections,  marking  the  variations  on  the  backs  of  centre 
stakes,  noting  the  elevations  of  roads,  stream  beds  and  high  water  lines, 
and  making  new  bench  marks  at  intervals  of  about  one  thousand  feet, 
preferably  near  the  sites  of  structures  and  heavy  cuts,  where  most 
needed,  and  out  of  the  way  of  probable  disturbance. 

2.  Then  traverse  the  line  again  with  the  transit,  over  the  old  points 
and  with  the  same  deflections  recorded  on  the  establishment  of  the  loca- 
tion if  found  correct,  trueing  the  interpolated  stakes  last  set  by  level, 
and  placing  and  referencing  centre  plugs  at  "grade"  pomts,  grade 
summits,  and  wherever  else  they  are  likely  to  be  convenient  during 
construction. 

3.  Any  discrepancies  in  line  or  level  with  former  work,  discovered 
during  these  operations,  should  be  reported  immediately  to  the  division 
engineer. 

4.  Slope  staking  follows  next  in  order.  Division  engineers  shall 
personally  ascertain  the  probable  character  of  the  material  in  excavations, 
boring  or  sinking  test  pits  when,  in  their  judgment,  the  importance  of 
such  knowledge  warrants  it ;  and  they  will  instruct  their  subordinates 
as  to  the  formation  slopes  to  be  adopted  in  every  questionable  case. 

5.  In  addition  to  setting  the  usual  grade  and  slope  stakes,  the  ground 
should  be  cross-sectioned  a  sufficient  width  to  provide  for  possible  slips, 
further  changes  of  slope,  or  a  four-track  road.  Stakes  or  plugs  should  be 
firmly  driven  at  these  limit  points  of  observation,  whether  tlie  work  be  in 
cut  or  fill,  in  range  crosswise  with  the  centre  and  slope  stakes,  which 
should  always  be  placed  at  right  angles  to  the  road  axis,  their  distance 
from  centre  line  and  elevations  as  to  grade  being  noted  for  record,  and 
for  use  if  needed  subsequently.  They  may  prove  to  be  very  convenient 
during  construction  at  cuts  through  uncertain  material,  and  when 
measuring  for  estimates. 

6.  On  hillsides  where  the  road  bed  is  partly  in  excavation  and 
partly  in  embankment,  its  dimensions  shall  be  compounded  of 
those  given  in  the  standard  drawings  for  excavation  and  embank- 
ment. 

7.  Borrow  pits,  grading  at  st  itions,  ditches,  and  all  other  incidental 


70  STRUCTURE  PLANS. 

excavations,  should  be  staked  and  recorded  with  the  same  exactness 
as  the  road  formation.  They  should  be  worked  in  a  regular  manner,  so 
as  to  be  readily  measured,  and  present  a  shapely  appearance  after  com- 
pletion. 

8.  Masses  of  rock  found  in  cuts  and  isolated  from  the  slopes  should  be 
measured  and  recorded  in  the  proper  books  and  shown  in  the  cross-section 
drawings. 

9.  The  accurate  establishment  and  subsequent  protection  of  tunnel 
lines  should  claim  the  early  personal  attention  of  division  engineers. 
They  will  be  duly  authorized  by  the  chief  engineer  to  acquire  the 
temporary  use  of  ground  for  observatories  and  guide  lines  outside  the 
Company's  right-of-way,  when  expedient  to  do  so. 

10.  The  alignment  and  levels  at  tunnel  sites  should  be  retraced  and  re- 
peated until  the  possibility  of  error  is  reduced  to  an  unimportant  mini- 
mum. Such  work  is  best  done  early  in  the  day,  while  the  air  is  equable 
and  free  from  refractory  currents. 

11.  Resident  engineers  shall  personally  attend  to  the  staking  of  all  found- 
ation pits.  Before  masonry  is  started,  the  division  engineer  should  inspect 
such  pits,  and  assure  himself  by  sounding  or  otherwise,  that  they  are  of 
sufficient  depth  and  firmness.  "When  judged  prudent,  the  bottom  earth 
should  be  compacted  with  rammers. 

12.  Currently  with  the  foregoing  operations,  the  location  record,  pre- 
scribed in  (II.,  5,)  should  be  perfected  by  the  addition  of  the  cross-section 
notes,  and  the  latter  line  and  level  notes,  and  all  permanently  entered  in 
ink. 

13.  Division  engineers  should  traverse  their  charges  weekly.  Resident 
engineers  should  be  constantly  on  the  line  by  day,  excepting  when  foul 
weather  or  important  office  work  prevents.  They  should  give  grade  and 
line  weekly,  and  whenever  asked  by  contractors.  They  are  thus  in  the 
way  of  correcting  errors  at  the  outset,  of  instructing  foremen  seasonably 
to  prevent  errors,  and  of  ascertaining  the  various  character  of  material 
for  estimates,  to  the  furtherance  of  the  work  and  the  due  service  of  the 
contractors,  who  should  not  have  reasonable  ground  for  dissatisfaction 
with  this  department. 

V.   STRUCTURE  PLANS. 

1.  The  chief  engineer  will  cause  standard  drawings  o^  the  road  forma- 
tion and  ordinary  structures  to  be  f  m-uished  to  each  division  office.    Di- 


FIEILD  AND  OFFICE  RECORDS.  71 

vision  engineers  shaU  supply  duplicates  of  these  drawings  to  their  resident 
engineers,  as  needed. 

2.  Division  engineers  shall  cause  necessary  modi.ications  to  be  made 
in  masonry  plans  to  adapt  them  to  various  localities,  altering  the  flare  or 
length  of  wing  wall,  for  example,  to  fit  irregular  ground,  skewing  for 
oblique  channels  or  roads,  sizing  for  heights  intermediate  to  those  pro- 
vided for  in  the  standards,  and  the  like  ;  but  the  elevations  and  square 
widths  of  bridge  seats  shall  not  be  altered  except  by  warrant  from  the 
chief  engineer  or  his  associate. 

3.  Special  instructions  will  be  given  as  to  structures  on  steep  in- 
clines and  skew  openings  sharper  than  forty-five  degrees  from  the  centre 
line. 

4.  Plans  modified  by  division  engineers,  and  also  the  standard  struc- 
tures which  they  propose  as  being  anywhere  suitable,  shall  have  the 
approval  of  the  chief  engineer  or  his  associate  before  the  work  is  laid 
out. 

5.  Where  special  structures  are  required,  such  as  viaducts,  large 
bridges,  or  other  exceptional  work,  not  provided  for  in  the  standard 
plans,  the  division  engineer  shall  cause  the  ground  to  be  surveyed  and 
mapped  to  five  feet  contours  ;  scale,  ten  feet  to  an  inch,  with  correspond- 
ing profile,  and  submit  the  same,  accompanied  by  illustrative  notes  and 
such  suggestions  as  he  may  think  proper  to  add,  to  the  associate 
engineer,  who  will,  thereupon,  cause  a  plan  to  be  made,  or  give  orders 
for  its  making  to  the  division  engineer.  Exhibits  of  this  kind  should 
include  high  and  low  water  marks,  character  of  bottom  or  sub-soil,  and, 
in  the  cases  of  road-crossings,  a  profile  of  the  same  for  five  hundred  feet 
each  way.  *■ 

6.  All  plans  of  railroad  buildings  shall  originate  at  the  central  office, 
and  copies  thereof  will  be  furnished  by  the  chief  engineer  or  his  associate, 
with  suitable  instructions,  to  the  division  or  principal  assistant  engineer 
charged  with  their  erection. 

7.  Copies  of  all  plans  prepared  by  division  engineers  for  their  residents 
shall  be  preserved  in  the  division  office. 


VI.   FIELD  AKD  OFFICE  RECORDS. 

1.  Eesident  engineers  fchall  prepare  a  series  of  cross-section  dra\yings, 
including  the  tunnels,  of  their  respective  subdivxjons,  in  bound  books  of 
uniform  size  furnished  for  that  purpose,  showing  the  original  surface  of 


73  FIELD  AND  OFFICE  RECORDS. 

the  ground  as  widely  as  observations  extend,  the  slope  staking  for  road 
formation,  the  staking  for  incidental  excavations,  the  proposed  formation 
lines,  and  the  computed  quantities  before  grading,  in  India  ink;  copies,  or 
written  abstracts,  of  which  cross-sections  they  shall  transmit  to  the  divis- 
ion engineer  from  time  to  time  as  they  are  made,  marked  with  the  name 
of  the  division  and  other  distinguishing  particulars. 

2.  On  completion  of  each  road-section  the  resident  engineer  shall 
amend  and  perfect  his  original  cross-section  book  by  drawing  thereon,  in 
permanent  red,  the  actual  formation  as  completed,  showing  the  parting 
Imes  between  various  classes  of  material,  and  the  actual  quantities  of  said 
various  classes  as  contained  in  the  final  estimate  of  the  graduation  of  said 
road-section;  together  with  a  statement  of  the  cost  of  said  graduation  to 
the  contractors  and  the  Company,  which  amendments  the  division  engi- 
neer shall  thereupon  cause  to  be  incorporated  in  his  own  copies  of  the 
cross-sections,  after  revision  by  him,  and  shall,  when  requested,  or  on  the 
completion  of  the  work,  transmit  the  originals  to  the  associate  engineer, 
endorsed  with  his  approval. 

3.  The  statement  of  cost  to  the  contractor  should  comprise,  as  nearly 
as  can  be  ascertained,  the  value  per  item,  and  the  amount  of  labor, 
material,  use  of  tools  and  machinery,  superintendence  and  sundries, 
distributed  and  assigned  in  such  detail  as  infonnation  on  hand  shall  war- 
rant. The  statement  of  cost  to  the  Company  should  be  a  summary  of  the 
final  estimate. 

4.  The  cross-section  books  will  be  paged  with  consecutive  numbers;  no 
erasures  shall  be  made  Ln  them,  nor  shall  any  leaf  be  removed  therefrom 
for  any  cause  whatsoever.  If  errors  occur  cancel  the  page  in  such  manner 
as  not  to  obscure  the  errors,  and  use  the  next  page. 

5.  Resident  engineers  shall  also  prepare  a  series  of  masonry  drawings, 
on  white  paper  sheets  of  uniform  size  furnished  for  the  purpose,  in  which 
all  such  structures,  including  drain  pipes,  shall  be  rejjresented  on  a  scale 
of  four  feet  to  the  inch,  or  eight  feet  to  the  inch,  as  the  division  engineer 
may  prescribe  for  structures  of  various  magnitude.  Such  drawings  shall 
show  the  said  structures  in  plan,  elevation,  and  section  as  actually  built, 
inclusive  of  foundations,  foundation  pits,  substructure  if  any,  grade  line, 
and  elevations  of  leading  details.  There  shall  be  also  a  legend  on  the 
dra^vings  of  each  separate  structure,  stating  clearly  the  actual  quantities 
of  the  various  classes  of  work  included  in  the  final  estimate,  and  a  sum- 
mary, such  as  is  prescribed  for  graduation,  of  the  actual  cost  to  the  con- 
tractors and  to  the  Company. 


FIELD  AND  OFFICE  RECORDS-  tS 

6.  On  the  completion  of  each  subdivision  said  cross-section,  tunnel  and 
masonry  drawings  shall  be  transmitted  to  the  division  engmeer,  and  by 
him,  when  so  requested,  after  correction  therefrom  of  the  copies  on  his 
files,  transmitted,  with  his  approval  affixed,  to  the  associate  engmeer. 

7.  Each  drawing  of  the  two  sets  described  above  shall  be  exactly  local- 
ized, in  its  title,  with  the  name  of  the  division,  subdivison,  section,  sta- 
tion and  plus. 

8.  Each  division  engineer,  at  or  before  the  time  of  transmitting  his 
first  monthly  estimate,  shall  send  to  the  associate  engineer  a  complete 
profile,  on  mounted  "Plate  A,"  paper,  of  his  division,  showing  align- 
ments, gradients,  and  other  full  details  as  finally  established  for  construc- 
tion. 

9.  Then,  and  thereafter  with  each  monthly  estimate,  he  shall  forward 
to  the  associate  engineer  tracing  exhibits,  or  written  memoranda,  indi- 
cating the  condition  of  the  work  at  the  date  of  said  estimate,  from  his 
progress  profile,  in  order  that  the  progress  profile  in  the  central  office 
may  be  supplemented  to  match. 

10.  All  progress  profiles  shall  represent  the  work  done  during  each 
month  in  transparent  washes  of  color,  as  follows: 

January Carmine.  July, Scarlet. 

February  Green.  August Dark  Green. 

March Yellow.  September Orange. 

April Cobali  Blue.  October Purple. 

May, Burnt  Sienna.  November  Burnt   Umher. 

June Black.  December. Gray.' 

11.  Division  engineer  shall  cause  to  be  prepared,  on  mounted  white 
roll  paper,  a  complete  map  and  profile  of  his  division,  horizontal  scale 
four  hundred  feet,  vertical  scale  forty  feet  to  an  inch,  both  on  the  same 
sheet,  showing  the  centre  line,  grade  line,  and  land  lines,  of  the  road  in 
red,  streams  in  blue,  brick  and  frame  buildings  in  carmine  and  burnt 
sienna  respectively,  faintly  colored;  all  other  details  in  India  ink,  with  ten 
feet  contours  finely  drawn,  each  even  hundred  slightly  heavied,  and  the 
outer  limits  of  road  formation — that  is  to  say,  the  crests  of  cuts  and  the 
toes  of  fills — indicated  in  plan  by  dotted  lines.  This  document  to  lie  on 
the  stocks  in  the  division  office,  gradually  perfecting,  and  finally  in- 
cluding all  the  company's  lands  and  buildings,  together  with  such  sup- 
plemental plans,  to  larger  scales,  as  the  chief  engineer  shall  order,  of  town 
properties  or  particular  reaches  of  the  road,  whereupon  it  shall  be  filed 


u 


FIELD  AND  OFFICE  RECORDS. 


in  the  central  office  as  a  permanent  record.  The  above  map  should  em- 
brace, if  possible,  all  the  topography  obtained  during  the  surveys 
within  one  mile  on  each  side  of  the  located  line,  and  sliould  be  neatly  and 
accurately  executed. 

12.  Each  division  engineer,  contemporaneously  with  the  foregoing  map 
and  profile,  shall  cause  to  be  prepared  a  complete  record  and  description, 
by  sections,  of  the  finished  roadway  on  his  division,  after  the  following 
general  form,  to  be  furnished  from  the  central  office  : 

Div.  No ,    Sec.  No 


RT.    OB 

KLEVT. 

1. 

CROSS 

GRADUATION  C.  Y. 

WAY, 

§ 
1 

SECTIONS. 

.2 

a 

be 

< 

6 

L. 

R. 

a 

1 

1 

•a 

L. 

c. 

R. 

Rock. 
Loose  R. 

Earth. 
Embk. 

•6 
a 

1 

MASONRY  CLASSES  C.    YDS. 


DESCRIPTION  OF 


Misc.  Mas'7  struc- 
tures. 


Bridges  and 
viaducts. 


Miscell. 


Remarks. 


13.  To  the  record  of  each  road  section  shall  be  appended  a  summary 
or  the  final  estimate  for  said  section,  as  paid  by  the  company,  and  the 
column  of  remarks  shall  contain  the  miscellaneous  notes  from  office  rec- 
ords previously  compUed,  together  with  such  other  infonnation,  as  to 
boundary  monuments  oi  plusses,  bench  marks,  foundations  and  sundries, 
as  may  be  of  use  on  future  enlargements  of  the  road-bed  and  right-of-way. 

14.  Division  engineers  shall  require  periodically  from  their  subordi- 
nates the  data  necessary  for  the  compilation  of  this  record.  On  its  com- 
pletion they  will  entitle  it,  adding  a  brief  description  of  the  division,  its 
locality  and  terminal  p>omts,  and  transmit  the  record  to  the  associate 
engineer,  endorsed  with  their  approval,  for  the  company's  archives. 

15.  Resident  engineers  Fhall  keep  a  series  of  field  books,  to  be  called 
"  Construction  Notes."  one  of  which  shall  be  always  borne  about  them, 
and  used  for  recording  their  daily  doings,  noted  on  the  spot,  -with  day, 
date,  and  locality  specified.  In  these  books  all  field  operations  relating 
to  the  work  of  the  contractors  shall  be  calculated  and  entered,  such  as  the 
giving  of  line  or  grade,  setting  or  re-setting  cross-section  stakes,  laying 


FIELD  AND  OFFICE  RECORDS.  75 

out  tunnels  and  structures,  measurements  for  estimate,  dimensions  and 
depths  of  foundation  pits,  coffer-dams,  elevation  of  bridge  seats,  verbal 
orders  given  to  the  contractors  or  their  agents ;  in  short,  all  their  trans- 
actions and  observations  on  the  line,  together  with  a  diary  of  office  work. 
The  current  volume  of  this  series  should  be  delivered  to  the  rodman  for 
his  use,  if  charged  with  separate  field  duties,  in  case  of  the  absence  or 
disability  of  the  resident.  These  books  will  be  numbered  consecutively 
and  plainly  marked,  on  the  outside,  with  the  names  of  the  division  and 
subdivision,  and  the  periods  of  time  covered  by  them.  They  shall  be  pre- 
served with  great  care,  and  turned  in  to  the  division  engineer  on  the 
completion  of  the  respective  subdivisions,  or  when  called  for. 

16.  Resident  engineers  shall  use  and  preserve  bound  books,  to  be  fur- 
nished from  the  central  office,  instead  of  the  common  scratch-blocks,  for 
office  calculations,  drafts  of  estimates,  all  figuring  of  exhibits  or 
return  called  for  by  the  division  engineer,  and  statements  by  others  enti- 
tled to  them,  with  day  and  date  noted  at  the  time  of  each  entry.  These 
books  shall  be  called  "  Blotters,"  and  shall  be  numbered  and  marked  as 
prescribed  for  "  Construction  Notes." 

17.  Division  engineers  shall  keep  similar  books  for  the  record  of  their 
daily  doings  in  the  office  or  field,  and  these,  together  with  those  of  the 
resident  engineers,  shall  be  delivered  by  them  to  the  associate  engineer, 
on  the  completion  of  the  work,  or  when  called  for.  "Construction 
Notes"  and  "  Blotters"  shall  be  Isit  in  the  original  manuscript,  and  not 
inked  over  in  pencil.  If  errors  occur,  cancel  in  such  manner  as  to  leave 
them  legible,  and  insert  the  coiTected  work  further  on,  noting  the  former 
as  erroneous,  and  referring  to  the  latter. 

18.  Division,  principal  assistant  and  resident  engineers  shall  preserve 
press  copies  of  all  official  written  communications  sent  out  by  them,  in 
bound  volumes,  to  be  properly  titled  and  indexed,  and  handed  into  the 
central  office  on  completion  of  the  work.  They  shall  indorse  and  preserve 
aU  like  communications  received  to  the  same  end. 

19.  Principal  assistant  and  division  engineers  will  be  supplied  with 
copies  of  the  contracts  and  specifications  relating  to  their  charges.  They 
may  be  commissioned  by  authority  of  the  chief  engineer  to  negotiate 
contracts  for  labor,  material  or  right  of  way  in  special  cases,  but  all  such 
contracts  must  be  conditioned  on  the  approval  of  the  chief  engineer, 
signed  by  himself  or  other  immediate  representatives  of  the  company,  and 
t'le  oiignals  filed  in  the  central  office. 


76  INSPECTORS  AND  TIME  KEEPERS. 

20.  All  subordinates  of  this  department  responsible  for  the  right  con- 
duct of  work,  shall  hold  the  contractors  to  its  timely  and  proper  execu- 
tion, in  accordance  with  the  tenViS  of  the  agreement  and  the  requirements 
of  the  specification.  They  should  not  only  be 'vigilant  to  prevent 
any  hindrance  to  the  contractors,  but  active  and  prompt  to  keep  well  in 
advance  of  them,  so  that  there  shall  be  no  just  cause  of  complaint  for 
lack  of  stakes  or  instructions.  All  ofiicial  communications  to  the  con- 
tractors should  be  clear  and  explicit,  and  respectful  in  tone,  and  should 
be  recorded  at  the  time,  as  herein  elsewhei:e  dii-ected.  Orders  and  in- 
structions shall  be  given  in  writing,  when  asked  for  by  any  contractor, 
sub-contractor  or  foreman. 

21.  Should  it  appear,  in  any  case,  that  the  conditions  of  a  contract  are 
likely  to  fail  of  fulfillment  as  to  time  of  completion  or  otherwise,  the  as- 
sociate engineer  shall  be  seasonably  informed  of  it,  with  a  statement  of 
the  causes.  Any  radical  remedies  provided  for  in  the  contract  nmst  be 
administered  by  the  chief  engineer  only,  or  by  express  authority  from 
him. 

22.  All  maps,  drawings,  papers  and  books  should  be  clearly  marked 
with  titles,  numbers  and  characters,  and  orderly  bestowed  and  cata- 
logued for  ready  reference  in  the  offices  of  this  department.  Division  en- 
gineers should  see  that  their  subordinates  conform  to  this  rule,  and  they 
should  at  frequent  intervals  inspect  the  instruments  furnished  their  sub- 
divisions, to  make  sure  that  they  are  kept  in  adjustment  and  not  ill- 
used. 

23.  No  original  records  shall  be  permitted  to  leave  the  respective  ofSces, 
excepting  as  herein  prescribed.  Other  departments  or  agencies  of  the 
company  entitled  to  information  from  this  department  must  be  served 
by  copy  only,  and  not  by  the  original  drawings,  sections  or  records,  unless 
the  chief  engineer  expressly  warrants  a  deviation  from  the  rule. 

24.  All  regulations  herein  contained  for  the  government  of  line  engi- 
neei-s  proper  shall  govern  principal  assist  ants  and  others  in  the  special 
service  of  the  department,  to  whom  they  are  cleary  applicable. 


Vn.  INSPECTORS  AND  TIME  KEEPERS. 

1.  Division  engineers  will  be  authorized,  when  it  appears  proper  to  the 
chief  engineer,  to  employ  inspectors  for  important  structures.  Such  in- 
spectors shall  receive  orders  from  and  report  directly  to  the  resident  en- 


ESTIMATES.  77 

gineer.     Division  engineers  will  instruct  their  residents  as   to  the  duties 
of  inspectors. 

2.  Each  division  engineer  may,  by  like  authority,  employ  a  general 
time  keeper,  whose  dnty  it  shall  be  to  keep  a  correct  record  of  the  labor 
and  machinery  employed  on  the  work,  properly  classified  and  located, 
tha  wages  paid,  materials  expended,  and  other  notes  concerning  the  prog- 
ress of  the  work  and  the  contractor's  outlay. 

3.  The  time  keeper  shall  act  under  the  immediate  orders  of  the  divi- 
sion engineer.  Resident  engineers  and  their  subordinates  should  be  in- 
structed to  co-operate  with  him,  and  he  shall  have  power  to  employ 
additional  help,  subject  to  the  approval  of  the  division  engineer,  in  the 
event  of  their  assistance  proving  inadequate. 

4.  He  should  report  weekly  to  the  division  engineer,  and  hand  in  a 
monthly  statement  of  the  force  account  of  each  subdivision,  properly 
distributed,  for  reference  by  the  division  engineer  of  the  residents. 

5.  Resident  engineers  and  their  subordinates  should  be  so  con- 
stantly on  the  line  as  to  obtain  an  independent  force  account,  approxi- 
mately correct,  for  themselves.  This  they  shall  do,  for  comparison  with 
that  furnished  by  the  division  engineer,  should  a  general  time  keeper 
be  employed  ;  and,  in  case  of  any  unaccountable  discrepancy,  call  his 
attention  to  it. 

6.  Division  engineers  shall  make  monthly  returns  of  force  accounts, 
with  their  monthly  estimates  to  the  associate  engineer,  after  a  form  i)ro- 
vided  by  the  central  office. 

7.  Division  engineers  shall  keep  a  book  of  force  accounts,  showing  the 
items  properly  classified  and  distributed,  and  willcompare  and  harmonize 
notes  with  the  Residents  when  making  up  the  Road  Section  Records 
herein  prescribed  (VI.  12). 


Vin.    ESTIMATES. 

1.  On  or  about  the  27th  of  each  month,  resident  engineers  shall  take 
measurements  and  make  an  estimate  of  the  work  done  on  each  section  of 
their  respective  subdivisions  during  the  month  current,  statements  of 
which  estimates  they  shall  prepare  in  duplicate  on  prescribed  forms, 
one  copy  to  be  retained,  the  other  to  be  delivered  to  the  division  engi- 
neer not  later  than  the  first  day  of  the  month  following  that  to  which 
they  refer. 


78  ACCOUNTS.  SUPPLIES  AND  SUNDRIES. 

2.  Division  engineers  shall  prepare  like  estimates  of  the  work  done  on 
each  section  of  their  respective  divisions  in  quadruplicate  and  send 
three  copies,  duly  authenticated,  to  the  associate  engineer,  not  later 
than  the  fifth  day  of  the  month  following  that  to  which  they  refer, 
accompanied  by  a  force  account,  a  recapitulation  of  work  after  such 
forma  as  may  be  provided,  and  abstracts  for  the  progress  profile  herein 
before  described  (VI. ,  9).  One  copy  of  the  estimate  sheets  and  accom- 
panying papers,  excepting  progress  data,  will  be  retained  on  his 
office  file. 

3.  Quantities  greater  than  those  due  to  the  net  measure,  as  defined  by 
the  slope  staking,  the  masonry  plans  or  prescribed  tunnel  sections  shall 
not  be  allowed  in  either  the  monthly  or  the  final  estimates  ;  provided, 
however,  that  any  extra  expense  incurred  shall  be  clearly  the  result 
of  slovenly  conductor  violation  of  orders.  If  unsuitably  slope-staked,  if 
drawings  are  erroneous,  or  if  shps  occur  in  cuts  and  falls  in  tunnels  from 
causes  not  reasonably  to  have  been  forecast  and  prevented,  the  extra  work 
done  may  be  covered  by  estimate,  under  instructions  from  the  chief 
engineer. 

4.  In  classifying  estimates,  the  quality  of  masonry  and  the  character  of 
material  removed,  as  described  in  the  specifications,  shall  be  regarded  ex- 
clusively of  all  other  considerations.  If  any  case  of  losing  merit  occu*^, 
employes  in  this  department  must  bear  in  mind  that  such  case  is  for  the 
judgment  and  the  action  solely  of  those  who  pay  the  money,  the  engi- 
neer's duty  being  rigorous  adherence  to  the  requirements  of  the  contract 
and  specifications. 

5.  No  employes  of  this  department  shall  be  interested  in  any  contract, 
or  in  the  furnishing  of  contractors'  supplies  on  the  line  of  the  road,  or  in 
any  business  connected  therewith,  excepting  that  of  the  Company. 


IX.    A.CCOUNTS,  SUPPLIES  AND  SUNDRIES. 

1.  The  pay-rolls  and  expense  accounts  for  each  month  shall  be  pre- 
pared by  the  division  engineers  and  ti'ansmitted,  with  their  endorse- 
ments, on  or  before  the  fifth  day  of  the  month  following,  to  the  associate 
engineer. 

2.  After  approval  in  the  central  office,  checks  will  be  sent  to  the  division 
engineers  for  each  individual  to  whom  payment  appears  to  be  due,  and 
the  receipted  pay  rolls  and  expense  vouchers  shall  then  be  returned  to  the 
associate  engineer. 


MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS.  79 

3.  Division  engineers  shall  book  the  salary  and  expense  accounts  of 
their  respective  divisions  in  the  usual  form,  and  shaU  report  all  discharges, 
appointments  and  transfers  to  the  associate  engineer  at  the  time  of  such 
transactions. 

4.  The  fixed  salaries  of  the  employes  of  this  department  shall  be  in  full 
for  all  service  and  personal  expense,  excepting  necessary  outlays  on  the 
Company's  business,  for  transportation  and  subsistence,  by  division  engi- 
neers or  their  draughtsmen  when  called  away  from  the  Division  Head- 
quarters, and  by  resident  engineers  or  their  subordinates  when  called 
away  from  their  Subdivisions. 

5.  Division  engineers  shall  make  formal  requisition  on  the  as- 
sociate engineer  for  necessary  equipment  and  supplies.  They  shall  keep 
a  record  of  all  company  property  in  their  charge,  and  make  report  there- 
of quarterly, with  inventory  of  articles  on  hand  at  date  of  previous  report, 
received  since,  expended,  in  what  manner  or  service,  and  on  hand  at 
date  of  current  report,  adding  explanatory  remarks. 

6.  Under  the  head  of  incidental  expenses  shall  be  included,  and  item- 
ized, minor  outlays  for  stationary  and  priming,  office  rent,  fuel,  lights 
and  attendance,  tools  and  repairs  thereof,  postage,  telegraph  and  express 
charges,  messengei*s  on  special  errands  requiring  certainty  and  dispatch, 
and  such  smaU  stores,  needed  in  the  progress  of  the  work,  as  can  best  be 
obtained  on  the  ground.  la  these  matters,  and  in  the  conduct  of  their 
charges  generally,  division  engineers  are  expected  to  practice  a  watch- 
ful and  rational  economy  and  to  exact  it  of  their  sub  rdinates.  Incorrect 
estimates,  slovenly  records,  laziness,  drunkenness,  erroneous  field  work, 
bungling  use  of  instruments  to  their  injury,  squandering  of  road  supplies 
for  private  account  and  the  hke  should  be  followed  by  quick  riddance  of 
the  culprit, 

7.  Offices  should  not  be  lounging  places,  and  great  care  must  be  taken 
that  no  unauthorized  persons  have  access  to  books,  papers,  or  other  infor- 
mation relating  to  the  work. 

8.  No  person  appointed  to  or  discharged  from  the  company's  service  in 
this  Department,  shall  be  allowed  expenses  to  or  from  the  field  of  service. 


X.  MISCELLANEOUS   INSTRUCTIONS  AND  SUGGESTIONS. 

1.  In  slope  staking,  when  material  is  doubtful,  stake  for  rock.  In  such 
cases  where  earth  cuts  are  started  vertical,  have  a  force  to  follow  closely 
with  trimmed  slopes,  to  avoid  irregular  breaks  and  shps.     Set  side  stakes 


80  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

every  fifty  feet  for  trimmers.  After  stripping  rock  restake  for  it.  Leave 
a  berm  of  foiir  feet  between  foot  of  earth  slope  and  crest  of  rock  in  mixed 
cuts. 

2.  All  curves  should  be  slope-staked  at  intervals  of  fifty  feet. 

3.  Where  cut  is  in  excess,  have  it  wasted  regularly  along  the  convexed 
side  of  curve  in  adjacent  fill,  unless  the  possibility  of  flattening  the  curve 
in  futiire  makes  it  expedient  to  waste  on  the  concave  side.  Waste  sym- 
metrically on  tangents  ;  if  single  track,  on  double  track  side, — subject 
to  the  condition  that  no  overhaul  shall  be  required  and  no  increase  of 
masonry,  except  by  warrant  from  the  central  office. 

4.  Where  fill  is  in  excess  on  single  track,  first  double  track  the  adjacent 
cuts  for  a  supply,  if  earth,  and  within  overhaul  limit.  Should  more  ma- 
terial be  needed,  widen  earth  cuts  to  their  utmost,  leaving  in  every  case 
room  for  berm  ditch  and  additional  four  feet  for  fence  berm. 

5.  Waste  no  material  above  grade  unless  imperative  and  authorized  by 
the  division  engineer.  Where  material  is  permitted  thus  to  be  wasted, 
leave  in  every  case  a  berm  of  not  less  than  ten  feet,  and  additional  allow- 
ance for  future  extra  track. 

6.  Be  vigilant  to  prevent  tresspass  on  adjacent  properties  in  making 
side  ditches,  spoil  banks,  or  otherwise. 

7.  Side  and  berm  ditches  should  be  opened  in  advance  of  graduation 
and  kept  open.  Material  from  berm  ditches  should  be  ridged  up  regularly 
on  down  hill  side;  that  from  side  ditches  deposited  in  embankment.  See 
that  the  outfall  from  ditches  in  cuts  is  turned  aside  so  as  not  to  scour  the 
fills. 

8.  Where  stream  channels  are  changed  the  new  channel  should  be  side 
sloped,  and  a  berm  of  twelve  feet,  with  allowance  for  future  extra  track, 
left  between  its  crest  and  foot  of  embankment. 

9.  On  bare  slopes,  to  be  embanked,  plow  the  ground  lengthwise  before 
filhng  in,  and  on  very  steep  hillsides  excavate  terrace  benches  to  hold  the 
embankment. 

10.  Examine  embankment  sites  for  springs  and  have  them  carefully 
drained  clear  of  the  formation,  by  ditches  filled  with  broken  stone  or 
cobbles. 

11.  Finish  all  eatth  or  mixed  embankments,  fiill  width  at  top  and  four 
per  centum  of  the  record  center  height  above  grade  for  the  reception  of 
ballast;  rock  embankments,  two  per  centum.  This  is  tentative,  and  sub- 
ject to  modification.    It  is  believed  to  be  sufficient  allowance  for  embank- 


MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS.  81 

ments  made  in  layers  or  with  scraper,  and  approximately  correct  for 
heavy  dumped  work  on  good  bottom,  which,  advancing  more  slowly,  must 
neeSs  have  gotten  to  its  bearing  in  some  measure  before  completion. 
Division  engineers  are  invited  to  give  their  past  experience  on  this  point, 
and  also  to  profit  by  their  present  opportunity  for  more  knowledge  con- 
cerning it. 

12.  In  rock  cuts  see  that  no  large  masses,  dislodged  by  blasting,  are  al- 
lowed to  remain  on  the  slopes  or  overhanging  them.  Examine  all  such 
masses  with  bars,  and,  where  liable  to  be  washed  or  frosted  down,  have 
them  removed  and  duly  entered  in  the  estimates, 

13.  Require  rock  cuts  and  tunnels  to  be  taken  out  full  width  and  depth 
at  once,  and  suifer  no  bottoming  to  be  left  over  except  by  special  permis- 
sion of  the  chief  engineer,  in  tunnels  only,  for  the  purpose  of  drainage 
during  construction. 

14.  See  that  the  road  is  graded  true  to  line,  and  as  staked  out ;  that 
material  needed  elsewhere  is  not  wasted  at  mouths  of  cuts  ;  that  side 
slopes  in  excavations  are  plane  surfaces,  not  convex  ;  that  embankments 
are  carried  out  the  full  width  due  to  the  slope  staking  at  whatever  level 
built ;  that  their  slopes  are  plane  surfaces,  not  concave  ;  that  they  are 
buUt  in  layers  back  of  all  abutment  and  culvert  walls  ;  that  the  centres 
of  arch  culverts  are  allowed  generally  to  remain  until  the  embankment 
has  been  carried  by  them  ;  and,  if  removed,  that  the  embankment  is 
built  in  layers  a  proper  height  above  crown  of  arch. 

15.  Approaches  to  crossings,  in  excavation  or  embankment,  should  be 
graded  not  less  than  twelve  feet  wide  on  top,  and  up  to  the  height* of  top 
of  raU— say  two  feet  above  the  grade  of  formation  ;  they  should  ramp  or 
slope  at  a  rate  not  exceeding  one  in  ten,  and  be  level  a  sufficient  distance 
each  side  of  the  railroad  to  prevent  the  possibility  of  stone  or  timber 
trucks  stalling  on  the  track. 

16.  Meeting  grades  should  be  rounded  off  with  vertical  curves  at  least 
six  himdred  feet  long;  and  as  much  longer,  especially  in  the  case  of  pock- 
ets, or  cyhndrical  grades,  as  economical  conditions  will  permit.  Special 
instructions  will  be  given  on  this  subject. 

17.  Be  cautious  not  to  allow  full  measure  in  monthly  estimates  before 
the  work  is  settled,  surfaced  and  trimmed;  a  safe  reserve  should  be  held, 
usually  for  such  items. 

18.  In  retracing  line  during  construction,  or  after  graduation,  use  the 
original  turning  points  established  on  the  final  revision  of  the  line. 


82  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

19.  Timber  and  brush  should  be  cleared  the  full  width  of  right-of- 
way,  and  valuable  timber  piled  up  along  the  right-of-way,  and  saved 
for  the  company,  where  the  clearing  is  done  by  the  contractor.  Tree*  en 
abutting  properties  whose  accidental  fall  might  encumber  the  track, 
should  be  legally  condemned  and  felled. 

20.  Avoid  small  openings  in  the  roadbed,  using  box  or  arch  culverts 
preferably. 

21.  The  road-bed  should  be  trimmed  tea  crown  of  three  inches  above 
grade  in  the  middle,  to  promote  lateral  drainage  under  the  ballast. 

22.  Sound  doubtfxil  foimdation  pits  with  an  iron  rod,  and  make  sure 
of  a  good  bottom.  Drain  them  when  feasible.  Where  not  liable  to  wash 
or  to  subsequent  exposure,  two  feet  of  gravel,  shingle  or  broken  stone, 
well  rammed,  makes  an  excellent  foundation  course. 

23.  See  particularly  to  the  deep  and  safe  founding  of  walls  and  curbs 
at  the  outfall  end  of  di"ainage  structures. 

24.  Before  sizing  opens  for  culverts  and  bridges  search  the  water  down 
stream  for  some  point  where  flood  volume  is  well  marked,  and  work  by 
that. 

25.  Observe  and  report  streams  suitable  for  water  supply. 

26.  Insist  on  specification  requirements  in  masonry.  Make  it  clearly 
understood  that  no  excess  of  neat  work  beyond  scale  plans  will  be  esti- 
mated. No  crushable  chips.  No  grouting  unless  specially  authorized. 
Flush  up  solid  instead,  with  mortar  as  stiff  as  it  will  work  readily.  Good 
bond  imperative,  and  to  take  precedence  of  outside  looks. 

27.  Clear  away  the  surplus  stone  and  wreckage  from  masonry 
sites  after  the  jobs  are  done ;  and  before  the  completion  of  each 
section,  have  blasted  rock  and  all  other  cumber  accumulated  during 
construction  removed  from  adjacent  properties  and  highways. 

28.  In  establishing  outside  tunnel  lines  by  daylight,  the  best  time  has 
been  found  to  be  just  after  sunrise,  and  the  best  sight  pole  a  half -inch 
round  iron  rod  painted  white.  Plummet  lamps,  on  clear  calm  nights, 
have  given  better  results  than  sight  poles  by  day,  being  distinctly  visible 
at  long  distances. 

29.  To  transfer  Une  down  a  shaft,  set  transit  point  at  a  distance  there- 
from of  about  twenty-five  feet,  from  which  point,  with  a  long  foresight 
two  staples  or  other  guides,  may  be  ranged  on  the  side  timbers  overhang- 
mg  the  pit,  and  the  centre  line  thence  plumbed  to  the  bottom  with  fine 


MISCELLANEOUS  INSTRUCTIONS  AND  SUGGBSTICNS.  83 

copper  wires,  bobbed  as  heavily  as  they  can  bear,  the  bobs  immersed  in 
water.  It  has  been  necessary  in  some  cases  to  box  in  the  wires,  to  pro- 
tect them  against  water  and  air  currents.  Careful  manipulation,  patient 
and  repeated  observations,  and  a  discreet  average  of  them  are  required 
for  a  correct  transfer. 

30.  The  range  at  bottom  must  be  transferred  to  wooden  roof  plugs,  in 
which  eyescrews,  staples  or  other  suitable  fixtures  are  ranged,  and  from 
which  plummet  lamps  may  be  hung  when  required. 

31.  Bench  marks  are  established  similarly  in  the  roof,  being  stubs  of 
steel  fastened  into  holes  or  chinks,  the  elevations  of  which  are  obtained 
by  means  of  a  reversed  rod.  The  levels  may  be  transferred  from  the 
surface  with  a  steel  tape  or  wooden  rods. 

33.  All  centre  points  and  bench  marks  should  be  placed  out  of  danger 
from  rocks  thrown  by  blasting. 

33.  Standard  measures  should  be  made  at  the  outset  by  which  to  test, 
from  time  to  time,  the  tapes,  level  rods  and  other  field  measures  used  on 
the  work,  as  it  is  important  that  these  measures  be  uniform,  and  guarded 
against  change. 

34.  For  leveling  underground  a  target  with  a  diamond-shaped  opening 
in  it  has  been  found  convenient,  one  of  the  diagonals  of  said  opening  being 
horizontal.  The  rod  is  plumbed  with  a  portable  level  bubble  made  for 
the  purpose,  and  a  light  is  held  behind  the  target  at  the  time  of  observa- 
tion. 

35.  Division  engineers  will  supplement  these  general  memoranda  as  to 
tunnel  surveying,  and  will  find  room  for  their  ingenuity  in  expanding 
and  diversifying  them  to  suit  various  practice. 

36.  Require  tie-<Jontractors  to  pile  the  ties  regularly,  both  ends  visible, 
and  spaced  suitably  for  inspection,  within  not  less  than  fifteen  feet  nor 
more  than  forty  feet  from  the  centre  line  of  double-track  road  bed,  and 
not  over  two  feet  below  grade,  when  the  nature  of  the  ground  will 
admit  of  compliance  with  this  rule.  When  it  will  not,  then  require  them 
to  be  delivered  and  piled  where  they  can  be  conveniently  got  at  by  the 
tracklayers. 

37.  After  tracklaying,  and  before  opening  the  road  to  trafiic,  a  flat  car 
should  be  run  its  whole  length  each  way,  with  templates,  fixable  cross- 
wise, for  testing  the  clear  width  of  rock  cuts  and  dimensions  of  tunnel 
sections.    Every  point  encroaching  on  the  standard  section  should  be 


84  MISCELLANEOUS  INSTRUCTIONS  AND  SUGGESTIONS. 

marked  with  red  paint  from  a  large  "  whitewash"   brush,   and  removed 
promptly  by  a  floating  gang. 

38.  The  terms  "  grade  line  "  and  '•  grade,"  as  herein  used,  refer  to  the 
surface  of  the  road  bed,  at  the  established  profile  grade  ;  that  is  to  say, 
to  the  bottoms  of  cuts  and  the  tops  of  fills,  as  prepared  for  the  reception 
of  any  crowning  to  promote  lateral  drainage  and  of  the  railway  proper, 
or  superstructure,  comprising  ballast,  ties  and  rails.  The  term  subgrade 
is  omitted  as  superfluous  and  confusing,  and  is  not  to  be  used  on  this 
road.  The  elevations  of  bridge  seats,  bridge  structures  and  their  p^rts. 
foundations,  piers,  trestle-work,  rails,  cross-ties,  and  all  other  details 
requiring  such  reference  shall  be  referred  to  the  elevation  of  "  grade,"  by 
plus  and  minus  signs. 

39.  Some  of  the  rules  contained  in  this  article  are  intended  to  be  sug- 
gestive rather  than  mandatory — practical  hints  and  instructions. 
Division  engineers  and  all  others  concerned  are  invited  to  report  any 
discrepancies,  errors  or  deficiencies,  which  they  may  observe,  either  here 
or  elsewhere,  in  the  present  compilation,  and  to  suggest  what  they  judge 
to  be  improvements,  corrections  or  useful  additions.  Regard  any  rules 
as  invalid  which  may  appear  to  conflict  with  provisions  in  the  contract 
and  specifications,  or  to  call  for  expense  not  therein  contemplated. 

WM.  F.   SHUNK, 
Approved  :  Associate  Engineer. 

ROBT.   H.   SAYRE, 

Chief  Engineer. 


FIELD  NOTES.  85 

INSTRUCTIONS     TO    DIVISION    AND     ASSISTANT     ENGI- 
NEERS RELATIVE  TO  FIELD  NOTES  ON  SURVEYS 
FOR  THE  SOUTH  PENNA.  R.  R.  CO. 


First— Enter  the  names  of  the  Division  Engineer,  Senior  Assistant  Engineer 
in  charge  of  the  party.  Assistant  Engineer  at  Transit  Instrument,  Assistant 
Engineer  at  Leveling  Instrument,  Hodmen,  Chainmen,  Flagman,  Axemen, 
composing  the  party.  Rodmen  must  make  the  same  notes,  also  enter  the 
date  and  place  vyhere  the  work  is. 

Socond— State  in  the  column  of  remarks  on  the  first  or  second  page  of  the 
book  at  the  beginning  of  the  notes  of  any  survey  or  levels,  the  letter  of  the 
line  and  where  it  was  begun  and  where  it  is  to  be  run  to. 

Third— The  Stakes  of  all  lines  must  be  numbered  on  the  rear  face,  next  to  the 
transit,  and  must  be  lettered  on  the  forward  face,  with  the  letter  of  the  line. 
A'l  lines  must  be  lettered. 

Fourth— State  what  Datum  the  Levels  start  from  or  refer  to,  and  if  started 
from  a  Bench  state  what  Bench  and  from  what  authority  or  book  the  Elevation 
was  obtained. 

Fifth— Enter  all  notes  of  Transit  or  Level  fully  and  distinctly  in  pencil  in  the 
field— if  any  details  or  calculations  are  omitted  from  haste  or  sudden  storms 
coming  up— make  them  complete  before  the  day  is  over,  and  when  required  by 
the  Senior  Assistant  or  Division  Engineer,  they  must  be  recorded  in  a  Record 
Book  the  same  evening. 

Sixth— All  field  notes  must  be  compared  during  the  day  taken,  and  all 
Levelers'  calculations  on  turning  points  must  be  made  by  Assistant  and  Rod- 
man, and  compared  on  the  spot  and  found  correct  before  going  forward  with 
the  work. 

Seventh— Benches  must  bo  made  at  least  once  in  every  mile,  and  oftener  if 
opportunity  offers.  Levels  must  be  tested  on  any  existing  Benches  found 
along  the  line,  and  tests  made  of  the  accuracy  of  the  old  and  new  works. 
Benciies  must  not  be  cut  on  shade  or  fruit  trees  and  no  unnecessary  damage 
done  in  clearing  the  line  of  sight ;  offsets  must  be  made  to  save  valuable  trees 

Eighth— In  passing  through  inclosed  land  the  Senior  Assistant  will  see  that 
th'^  fences  taken  down  by  the  party  are  put  up  after  they  pass  forward. 

Ninth— The  Assistant  at  the  Transit  must  record  the  names  of  land  owners, 
the  points  whiire  boundaries  are  crossed,  and  their  courses  when  obtainable. 

Tenth— Chiefs  of  Party  must  arrange  to  get  the  party  out  and  at  their  work  as 
early  as  possible  in  the  morning,  and  keep  them  employed  until  the  proper 
hour  in  the  evening.  All  preparations  for  the  field  work  must  be  made  by  the 
Senior  Assistant  and  Assistants  the  previous  evening,  so  that  no  delays  may 
occur  in  the  morning.  Dinner  will  be  procured  by  the  Senior  Assistant  to  be 
eaten  in  the  Held  when  the  party  is  more  than  one  mile  from  boarding  places. 

Boarding  expenses  paid  by  any  members  of  the  party  will  be  reported  to  the 
Senior  Assistant  and  will  be  repaid  by  the  company  at  the  end  of  the  month. 

Eleventh— Senior  Assistants  will  see  that  the  instruments,  rods  and  chains 
are  kept  in  good  order  and  adjustment  by  the  Assistants;  any  damage  to  in- 
struments or  rods  from  want  of  proper  care  must  be  defrayed  by  the  Assistant 
having  the  same  in  charge. 

Twelfth— Daily  notes  of  the  work  done  and  the  date  must  be  entered  in  this 
field  book  every  evening. 

Thirteenth— Assistant  Engineers  in  charge  of  the  Transit  must  plot  their 
lines,  and  Assistants  in  charge  of  the  Level  must,  with  the  aid  of  their  Rodman, 
make  a  profile  every  evening,  of  tiio  line  leveled  over  each  day. 

Fourteenth— Division  and  Senior  Assistant  Engineers  Avill  make  reports  of 
instruments  and  stationary  on  hand  at  the  close  of  each  month,  and  send  them 
in  promptly  to  the  General  Office. 

Fifteenth— Division  Engineers  must  report  any  neglect  of  these  instructions 
to  the  Chief  Assistant  Engineer. 

OuvEB  W.  Babnes,  Chief  Engineer. 


CHAPTER  IV. 


Topography,  and  Staking-out  Problems. 

TABLE  FOR  COMPUTING  RIGHT  OF  WAY  AREAS. 
Width  100  ft. 


.0 

.1 

.2 

.3 

0... 

0.000 

0.023 

0.046 

0.069 

1... 

0.230 

0.253 

0.276 

0.299 

2.. 

0.460 

0.483 

0.506 

0.529 

H... 

0.690 

0.713 

0.736 

0.759 

i... 

0.920 

0.943 

0  966 

0.989 

5  - 

1.150 

1.173 

1.196 

1.219 

6... 

1.380 

1  403 

1.426 

1.449 

7... 

i.ao 

1.633 

1.656 

1.679 

8... 

1.840 

1.863 

1.886 

1.909 

9.. 

2.070 

2.093 

2.116 

2.139 

10... 

2.300 

2.323 

2.346 

2.369 

11... 

2.530 

2.553 

2.576 

2.599 

12. 

2.760 

2.783 

2.806 

2.829 

13... 

2.990 

3.013 

3.036 

3.059 

14... 

3.220 

3.243 

3.266 

3.289 

15... 

3.450 

3  473 

3.J96 

3  519 

16. 

3.680 

3.703 

3.726 

3.749 

17  .. 

3.910 

3.933 

3.956 

3.979 

18.   . 

4.140 

•4.163 

4.186 

4.209 

1.4... 

4.370 

4  393 

4.416 

4.439 

20.   . 

4.600 

4.623 

4.646 

4.669 

21... 

4.830 

4.853 

4.876 

4.899 

22. . . 

5.060 

5.083 

5.106 

5.129 

2;^... 

5.290 

5.313 

5.336 

5.359 

24... 

5.520 

5.543 

5.566 

5.589 

25... 

5.750 

5.773 

5.796 

5.819 

26... 

5  980 

6.003 

6.026 

6.019 

27... 

6.210 

6  233 

6.256 

6.279  1 

28  .. 

6.440 

6.463 

6.486 

6.5'i9 

29. 

6  670 

6.693 

6.716 

6.739 

30. 

6.900 

6.923 

6  946 

6.969 

0.092 
0.322 
0.552 

0  782 

1  012 
1.242 
1.472 
1.702 
1.932 
2.162 
2.392 
2.622 
2.852 
3.082 
3.. 312 
3.542 
3.772 
4.002 
4.232 
4.462 
4.692 
4.922 
5.152 
5.382 
5.612 
5.842 
6.072 
6.302 
6.5.32 
6.762 
6.992 


0.115 
0.345 
0.575 
0.805 
1.035 
1  265 
1.495 
1.725 
1.955 
2.185 
2.415 
2.645 
2.875 
3.105 
3.335 
3.565 
3.795 
4.025 
4.255 
4.485 
4.715 
4.945 
5.175 
5.405 
5.635 
5  865 
6.095 
6.325 
6.555 
6.785 
7.015 


.6 

.7 

0.138 

0.161 

0.368 

0.391 

0.598 

0.621 

0.828 

0.851 

1.058 

1.081 

1.288 

1.311 

1.518 

1.541 

1.748 

1.771 

1.978 

2.001 

2.208 

2  231 

2.438 

2.461 

2.66S 

2.691 

2.898 

2.921 

3  128 

3.151 

3.358 

3.381 

3.588 

3  611 

3  818 

3.841 

4.048 

4.071 

4.278 

4.301 

4.508 

4.531 

4.738 

4.761 

4.968 

4.991 

5.198 

5.221 

5.428 

5.451 

5.658 

5.681 

5.888 

5.911 

6.118 

6.141 

6.348 

6.371 

6.578 

6.601  , 

6.808 

6.831 

7.038 

7.061 

0.184 
0.414 
0.614 
0.874 
1.104 
1.334 
1.5^ 
1.794 
2.034 
2.254 
2.484 
2.714 
2.944 
3.174 
3.4M 
3.634 
3.864 
4.094 
4.334 
4.554 
4.784 
5.014 
5.244 
5.474 
5.7M 
5.934 
6.164 
6.394 
6.624 
6.854 
7.084 


0.207 
0.437 
0.667 
0.897 
1.127 
1.357 
1.587 
1.817 
2.047 
2.277 
2.507 
2.737 
2.967 
3.197 
3.427 
3.657 
3.887 
4.117 
4.347 
4.577 
4.807 
5.037 
5.267 
5.497 
5.727 
5  957 
6.187 
6.417 
6.647 
6.877 
7.107 


Feet. 
.0023 
.0046 
.0069 
.0092 
.0115 
.0138 
.0161 
.0184 
.0207 
.0230 


Having  the  distance  between  the  boundaries  of  the  tract  through  which  the  line 
passes,  find  the  number  of  stations  in  the  left  hand  column  and  in  the  column  of 
tenths  under  .0  to  0.9  will  be  found  the  acres  required,  if  the  plus  is  an  even  10  ft.  If 
the  plus  contains  odd  feet  the  correction  to  be  added  is  found  in  the  column  of  feet. 


FIELD  WORK-LOCATING  CONTOURS.  8? 

TOPOGRAPHICAL  FIELD  WORK. 

The  topographical  party  consists  of  three  persons:  a  chief,  often  called 
the  topographer,  and  two  assistants,  called  the  levelman  and  the  rodman. 
The  field  work  is  generally  one  day  behind  that  of  the  transit  and  level 
[■arties  in  order  that  their  notes  may  be  utilized. 

The  topographer  is  provided  with  a  drawing  board  about  16  by  18 
inches,  having  raised  edges,  thus  forming  a  kind  of  box  14  by  16  inches, 
in  which  is  kept  several  sheets  of  paper  ruled  into  squares,  two  triangles, 
a  scale,  protractor  and  pencils,  the  whole  being  covered  by  a  leather  flap 
when  not  in  use.     He  also  carries  a  small  compass. 

The  levelman  carries  a  Locke  level,  which  can  be  mounted  upon  a  rod 
abouc  five  feet  long,  so  that  when  set  it  is  exactly  five  feet  above  the  sur- 
face of  the  ground.  This  rod  should  be  graduated  in  feet  and  tenths  from 
the  foot  upward,  and  it  is  sometimes  convenient  to  have  it  rectangular  in 
section,  so  that  it  can  he  used  as  a  slope  board.  He  also  carries  a  cli- 
nometer, and  a  note  book  having  the  right-hand  page  ruled  into  squares. 

The  rodman  carries  a  tape  line,  and  a  rod  either  10  or  15  ft.  in  length, 
plainly  graduated  in  feet  and  tenths,  the  zero  being  at  the  foot.  He  will 
often  find  it  convenient  to  carry  a  hatchet. 

METHOD  OP  LOCATINO  COJSTOURS. 

The  object  of  the  topographical  work  is  to  obtain  the  data  for  plotting 
the  contours  on  both  sides  of  the  line,  and  also  the  streams,  roads,  houses, 
and  other  natural  and  artificial  features.  The  general  custom  is  to  take 
contours  at  every  five  feet  of  vertical  height. 

When  the  transit  and  level  parties  have  finished  a  day's  work,  the  topog- 
rapher takes  their  field  books  and  plots  the  line  upon  his  sheets,  record- 
ing the  intersection  angles,  the  bearings,  the  elevations  of  the  stations  and 
of  the  streams  and  roads  crossed  by  the  line.  His  levelman  also  records 
the  same  elevations,  in  the  field  book,  arranging  the  notes  so  as  to  read 
upward  from  the  bottom  of  the  page. 

The  next  morning  the  topographical  party  starts  where  the  transit  and 
level  notes  began.  The  levelman  sets  his  Locke  level  at  the  first  station, 
which  we  will  suppose  to  be  No.  25,  whose  elevation  is  372.6  feet.  The 
height  of  the  instrument  is  then  377.6  feet.  The  rodman  moves  down  the 
slope  at  right  angles  to  the  line,  and  is  directed  to  stop  by  the  levelman 
when  his  line  of  sight  cuts  the  rod  at  7.6  feet.  The  foot  of  the  rod  is  then 
on  the  370  foot  contour,  and  its  horizontal  distance  from  the  station  is 
measured  and  recorded.    The  rodman  then  moves  down  until  the  level- 


88  TOPOGRAPHY,  AND  STAKING-OUT  PROBLEMS. 

man  reads  12.6  feet  on  the  rod,  when  its  foot  is  on  the  365  contour.  The 
levelman  must  now  move  to  this  last  point,  set  up  his  level,  and  the  rod- 
man  goes  down  the  slope  until  his  rod  reads  10.0  and  15.0  feet,  which  give 
the  860  and  355  contours  respectively.  The  process  is  thus  continued  as 
far  as  desired,  the  distance  to  each  contour  being  recorded  always  fi^-om 
the  station  for  convenience  in  subsequent  plotting  and  computations. 

In  going  up  the  slope  on  the  other  side  of  the  line  the  rod  should  be 
placed  at  station  25,  and  the  380  and  885  feet  contour  planes  then  cut  the 
rod  at  the  readings  7.4  and  12.4  feet  respectively.  The  levelman  goes  up 
the  slope  at  right  angles  to  the  line  and  sets  his  level,  so  that  the  line  of 
sight  reads  12.4,  when  he  is  on  the  880  feet  contour,  and  the  height  of  the 
instrument  is  385  feet.  The  rod  is  now  brought  forward,  and  the  other 
contours  located  and  recorded,  and  the  process  is  continued  as  far  up  the 
slope  as  desired. 

After  taking  the  contours  for  a  certain  distance  on  each  side  of  the  line 
at  a  station  some  topographers  make  a  note  of  the  general  slope  of  the 
ground  for  some  distance  farther,  measuring  the  inclination  by  the  clinom- 
eter and  slope  board. 

FIELD  NOTES. 

Notes  of  the  position  of  each  contour  at  each  station  are  kept  by  the 
levelman  on  the  left  hand  page  of  his  field  book,  the  manner  of  arrange- 
ment being  as  here  shown : 


200 

46 

22 

.15 

375.5 

2 

27 

8.6 

300 

50 

390 

385 

380 

26 

375 

380 

385 

4° 

200 

89 

49 

7 

372.6 

13 

40 

79 

104 

2M 

6° 

385 

380 

375 

25 

370 

365 

360 

355 

5° 

In  the  middle  column  are  placed  the  numbers  of  the  stations  and  their 
elevations  as  obtained  from  the  notes  oi  one  level  party.  In  the  right  col- 
umn are  given  the  distances  from  the  station  to  each  contour  on  the  right 
of  the  line,  it  being  18  feet  from  station  25  to  the  370  contour,  40  feet  to 
the  865  contour,  and  so  on.  The  last  entry  shows  that  the  ground  has 
the  uniform  slope  of  5  degrees  from  the  855  contour  to  a  distance  of  250 
foet  from  the  station.  In  like  manner  the  notes  of  the  contours  on  the 
left  hand  side  of  the  line  are  placed  in  the  left  column. 


FIELD  PLOTTING-LOCATING  BUILDINGS.  89 

FIFLD  PLOTTING. 

While  the  levelman  and  rodman  are  taking  these  notes  the  topographer 
plots  on  his  sheet  the  point  where  each  contour  is  located  at  the  right 
and  left  of  station  25.  Also  by  the  help  of  a  table  pasted  on  his  drawing- 
board  he  marks  the  points  where  the  contours  fall  on  the  uniform  slopes 
at  the  sides.  This  table  is  the  following,  giving  the  horizontal  distance 
in  feet  between  two  five  foot  contours  for  different  slopes  of  the  surface 
of  the  ground. 

Slope  of  surface 1°  2"  3°  4°  5°  6° 

Distance  between  contours,  feet...28G  143  95  72  57  48 

It  is  easy  to  prepare  a  more  extended  table,  since  the  distance  is  five 
times  the  natural  co-tangent  of  the  slope. 

The  party  then  moves  to  station  26  where  the  same  operations  are  re- 
peated, and  the  topographer,  orienting  his  drawing  board  (that  is,  placing 
the  plotted  line  parallel  to  the  line  as  run)  is  able  to  connect  the  corre- 
sponding contour  points  at  station  25  with  those  at  station  26.  With  a 
little  experience  this  can  be  done  in  the  field  to  a  far  greater  precision 
than  by  any  oflfice  work.  If  the  ground  is  irregular  between  stations  in- 
termediate work  may  be  necessary,  but  with  the  ground  in  front  of  his 
drawing  board  the  skilled  topographer  will  rarely  need  such  data  except 
when  necessary  to  be  noted  for  the  purpose  of  earthwork  estimates. 

The  record  kept  by  the  levelman  in  the  field  book  furnishes  the  means 
of  plotting  the  contours  in  the  office  in  case  a  sheet  of  topography  should 
be  lost,  and  it  will  also  be  needed  in  making  estimates  of  earthwork  which 
are  often  needed  in  deciding  upon  the  final  position  of  the  line. 

On  the  right-hand  page  of  the  field  book  the  levelman  or  the  topog- 
grapher  will  keep  the  record  of  all  the  distances  measured  to  streets, 
buildings,  fences  or  other  objects,  together  with  a  sketch  of  their  location. 
Some  of  these,  particularly  streams,  edges  of  marshes,  roads  and  winding 
fences,  he  may  also  prefer  to  plot  upon  his  sheets  in  the  field  instead  of 
waiting  to  do  it  in  the  office.  But  well-defined  objects,  such  as  houses 
and  straight  fences,  may  be  as  well  deferred  to  office  hours  if  the  topog- 
rapher is  pressed  for  time  in  the  field.  The  instructions  given  to  a  topog- 
rapher by  his  chief  or  locating  engineer  will  decide  in  regard  to  the-e 
details. 

LOCATING  BUILl.INGS. 

In  locating  buildings  young  topographers  generally  attempt  to  measure 
offsets  from  the  corners  at  right  angles  to  the  line.  This  is  only  advisa- 
ble where  the  sides  of  the  building  are  closely  parallel  and  perpendicular 


yO  TOPOGRAPHY,  AND  STAKING-OUT  PROBLEMS. 

to  the  line.  If  a  building  stands  obliquely  to  the  line  it  will  be  best  to 
measure  the  offsets  obliquely  also  so  as  to  be  in  line  with  two  of  the  sides, 
but  the  bearings  of  the  oblique  offsets  should  be  noted  or  the  angles  which 
they  make  with  the  line.  On  preliminary  work  fences  can  be  determined 
by  compass  bearings  and  some  little  pacing,  and  in  all  kinds  of  work  it  is 
desirable  that  the  levelman  and  rodman,  as  well  as  the  topographer, 
have  the  ability  to  determine  pretty  accurately  the  length  of  a  line  by 
pacing. 

METHODS  OF  SETTING  SLOPE  STAKES. 
I. 
When  the  ground  at  a  station  is  level  the  slope  stakes  are  easily  set  by 
the  use  of  the  tape  alone. 
Let  B  —  width  of  road  bed. 
Let  C  =  center  cut  or  fill. 
Let  s  =  side  slope,  usually  1|  to  1. 
Then  the  distance  from  the  station  to  each  slope  stake  is 

H=iB  +  sC. 
For  example,  if  the  roadbed  is  18  feet  wide  and  the  side  slope  1^  to  1, 
the  distance  out  is 

fl"  =  9  +  li  C. 
If  C  =  6.2  feet,  the  distance  H  is  18.3  feet,  and  this  is  to  be  laid  off 
with  a  taper  on  each  side  of  the  station. 

n. 

When  the  ground  at  a  station  is  not  level  it  is  usually  the  custom  to 
find  the  position  of  the  slope  stake  by  successive  trials.  The  following  is 
the  method  as  generally  carried  out  in  the  field  : 

The  leveler,  having  obtained  the  amount  of  fill  required  at  the  station, 
which  we  will  assume  for  convenience  to  be  3  feet,  judges,  after  closely 
observing  the  ground,  that  the  fill  or  distance  of  the  ground  below  grade 
at  the  point  of  intersection  of  the  slope  with  the  natural  surface  which 
he  is  seeking,  is  about  9  feet  greater  than  at  the  center,  or  12  feet  in  all. 
K  this  supposition  be  correct,  the  point  required  will  be  at  a  distance  out 
equal  to  one  and  a  half  times  the  assumed  fill  plus  half  the  roadbed  at 
grade  ;  that  is.  if  the  altitude  E  E'  of  the  triangle  B  E  E  is  equal  to  12, 
then  its  base  B  E'  will  equal  18  (the  slope  being  such  that  each  foot  of 
altitude  or  fill  requires  one  and  a  half  feet  of  base),  and  the  total  dis- 
tance out  C  E\  will  be  the  base  B  P!'  plus  half  the  roadbed  (assumed  as 
^  feet),  or  18  +  9  =  27.    The  rodman  now  holds  his  rod  at  this  distance 


METHODS  OF  SETTING  SLOPE  STAKES. 


91 


out,  and  the  rod  reading  subtracted  from  the  H.  I.  gives  the  elevation  of 
the  ground  at  the  point,  and  this  elevation  subtracted  from  the  elevation 
of  grade  gives  the  fill  or  distance  of  the  point  below  grade.  Bat  the  fill 
at  27  feet  out,  instead  of  being  12  feet  as  was  assumed,  proves  to  be  but 
10  feet,  showing  that  a  point  twelve  feet  below  grade  is  below  the  natural 
surface,  and  therefore  beyond  its  point  of  intersection  with  required 
slope.  §ince,  therefore,  any  assumption  greater  than  13  feet  would  only 
carry  us  tiprther  from  the  desired  point,  let  us  assume  for  a  new  trial  a 
smaller  number,  say  6  feet,  with  corresponding  distance  out  of  6  +  f  +  9 
=  18  feet.  But  the  rod  having  been  held  at  this  new  distance  out,  we 
lind  the  depth  of  the  point  below  grade  to  be  7.6  feet,  instead  of  6  feet  as 
was  assumed,  and  holding  the  rod  anew  at  the  distance  out  correspond- 

f 


ing  to  a  fill  of  7.6  feet— that  is,  7.6  +  ^^  +  9  =  20.4  feet— we  find  the 
depth  of  this  new  point  to  be  8.4  feet  below  grade,  which  requires  a  still 
greater  distance  out— that  is,  8.4  +  ^  +  9  =  21.6  feet.  But  it  will  be 
observed  that  with  each  new  trial  the  difference  between  the  assumed 
and  calculated  distances  is  decreasing,  and  that  therefore  we  are  gradu- 
ally approaching  the  intersection,  and  are  very  near  it,  as  the  difference 
between  the  two  last  distances  was  very  small.  Adding  now  but  a  small 
quantity,  say  0.6  foot,  to  our  last  trial  fill,  which  was  8.4  feet,  we  have  9 
feet,  and  taking  a  rod  reading  at  the  corresponding  distance  out,  9.  +  | 
+  9  =  22.5  feet,  we  find  the  actual  distance  of  the  ground  below  grade  to 
be  9  feet,  and  that  the  measured  distance  out  agrees  with  the  calculated 
distance,  proving  the  last  assumption  to  have  been  correct,  and  the  stake  is 
now  driven  at  the  point  thus  found.  The  number  of  trials  or  approxima- 
tions necessary  to  determine  this  point  varies  with  the  regularity  of  the 
rise  or  fall  of  the  original  svirface,  and  with  the  experience  of  the  leveler. 

The  application  of  this  method  to  a  case  in  excavation  scarcely  needs 
a  separate  explanation,  the  same  prism  being  merely. inverted,  and  the 


92 


TOPOGRAPHY,  AND  STAKING-OUT  PROBLEMS. 


level  being  always  above  grade, 
instead  of  sometimes  above  and 
sometimes  below  as  in  embank- 
ment. 

III. 

When  a  large  amount  of  work  is 
to  be  done  in  side  slopes  of  1^  to  1 
it  is  sometimes  advantageous  to 
have  a  tape  graduated  with  dis- 
tances of  one  and  a  half  feet  mark- 
ed as  feet  over  a  part  of  its  length. 
The  cut  shows  the  method  both 
with  the  common  tape  and  with 
the  new  tape.  This  cut,  with  the 
following  description  of  its  use,  is 
taken  from  a  small  pamphlet  pub- 
lished by  Keuffel  &  Esser,  New 
York. 

Let  us  assume,  as  was  done  in 
the  explanation  of  the  common 
method,  that  in  descending  toward 
the  point  at  which  the  slope  stake 
is  to  be  set,  the  ground  has  fallen 
9  fc,  or  is  in  alll2  ft.  below  grade, 
that  is,  we  assume  that  the  dis- 
tance E  E' ,  or  its  equivalent  B  B  ', 
is  12  ft.;  if  this  is  correct,  the  point 
E  must  be,  in  order  to  satisfy  the 
conditions  of  the  slope,  at  a  dis- 
tance from  B"  equal  to  12  of  the 
divisions  of  our  new  tape  (see  Fig 
5),  or,  since  the  tape-ring  is  held  at 
the  center  stake  C,  E  must  be  18 
ft.  further  out  than  the  point  B, 
the  O  on  our  new  tape ;  which  be- 
ing nine  feet  from  the  ring,  had 
already  carried  us  out  to  5  .  But 
the  rodman  having  held  his  rod  at 
the  assumed  point,  that  is,  at  di- 
vision 12  of  the  tape,  the  leveler 


in  <h  n  Ljh. 


J  METHODS  OF  SETTING  SLOPE  STAKES.  93 

tells  him  that  the  fill,  instead  of  being  12  ft.  at  that  point,  as  was  supposed, 
is  but  10  ft.,  the  rodman,  therefore,  knowing  that  the  number  given 
him  by  the  leveler  indicating  the  amount  of  fill,  must  be  identical 
with  the  number  on  the  tape  indicatmg  distance  out,  that  is,  that 
the  number  of  the  divisions  of  the  vertical  line  must  be  the  same 
as  the  number  of  divisions  of  the  horizontal  line,  sees  at  once  that 
he  is  not  at  the  right  point,  but  that  he  is  too  far  out,  as  the  number  of 
divisions  on  the  tape  is  greater  than  the  number  of  divisions  in  the  height 
of  fill,  so  he  holds  at  a  new  point  further  in,  say  at  six.  The  leveler  hav- 
ing taken  a  rod-reading  at  the  new  point,  tells  the  rodman  that  the  fill 
there  is  7.6  ft. ,  and  the  rodman  tees  at  a  glance  that  he  is  not  at  the  right 
point,  since  the  horizontal  number  six  of  the  tape  does  not  agree  with  the 
vertical  number  7.6  given  him  by  the  leveler,  and  he  knows  that  he  is  too 
far  in,  and  therefore  tries  the  rod  at  a  point  further  out,  say  at  division 
9.  The  leveler  having  read  the  rod  at  the  new  point,  sings  out  "fill 
nine  feet,"  which,  befng  the  same  as  the  tape  reading,  the  rodman  knows 
he  has  found  the  right  point,  and  drives  the  stake.  It  will  be  observed 
that  the  only  calculation  the  leveler  has  had  to  make  for  each  of  these 
trials  has  been  simply  that  necessary  to  find  the  distance  below  grade  of 
each  trial  point,  the  rodman  having  found  his  own  distance  out  by  mere- 
ly glancing  at  his  tape,  prepared  for  that  purpose.  If  it  is  desired  to 
record  in  the  note-book  the  actual  distance  out  from  the  center  stake  it  is 
only  necessary  to  turn  the  tape  over  and  read  off  the  entire  length  of  the 
line  C"  ^  in  feet  and  tenths  as  usual. 

IV, 

When  the  surface  of  the  ground  at  a  station  has  a  uniform  slope  trans- 
versely, some  engineers  prefer  to  calculate  the  distances  out  of  the  slope 
stakes  by  formulas. 

Let  B= width  of  roadbed. 

Let  C=center  cut  or  fill. 

Let  <S= tangent  of  inclination  of  side  slope. 

Let  r=  tangent  of  inclination  of  cross  slope  of  ground. 

Then  the  distance  out  to  the  up  hill  slope  stake  in  cut,  or  to  the  down 
bill  slope  stake  in  full,  is 

„  _C+iSB 

and  the  distance  out  to  the  down  hill  slope  stake  in  cut,  or  to  the  up  hill 
slope  stake  in  fill,  is 

„      C+iSB 


94  TOPOGRAPHY,  AND  STAKING-OUT  PROBLEMS. 

The  quantity  i  SB  is  a  constant  quantity  for  each  given  roadbed  and 
side  slope.  For  example,  if  the  width  of  roadbed  is  18  feet,  and  the  side 
slope  is  1|  to  1,  then  ^  B=9  and  ^=|,  whence  -J  SB=6  and  the  formulas 
become 

and 

The  values  of  T  may  be  measured  directly  in  the  field  by  having  a  rod 
exactly  ten  feet  long  held  exactly  level  with  one  end  on  the  ground;  then 
the  vertical  distance  from  the  other  end  to  the  ground  is  ten  times  T;  or  if 
the  slope  be  observed  by  the  clinometer  in  degrees,  the  values  of  T  can  be 
taken  from  a  table  of  natural  tangents.  For  example,  if  the  uniform 
cross  slope  is  4i  degrees,  the  value  of  Tis  0.0787.  Then  if  C  is  6.2  feet, 
the  distances  out  are 

°^=  0.6667-0.0787  "^^'"^  *^*' 

^°^  °^  =  ^:6667-T0:0787=^^-2  ^"^*- 

If  the  surface  changes  its  slope  between  the  slope  stakes,  these  formu- 
las will  not  apply  except  approximately.  In  such  cases  the  method  of 
trial  can  alone  be  relied  upon  to  give  satisfactory  results. 


FLATTENING    A    CDRVE. 

Having  located  the  curve  E  F  G,  joining  the  tangents  A  B  and  B  C,  it 

is  desired  to  join  tha  tangents  by  another  curve  which  shall  pass  through 

the  point  L,  distant  a  from  F. 

g  Let  radius  E I  =  r,  radius  D  K  =  R,  F  L  =  a. 

Angle  at  center  =  2  6.     Draw  M  I  parallel  with 

AB. 

In  the  triangle  I  M  K  vre  have  angle  K  =  S. 

angle  M  =  90°.    Side  I K  =  R  +  a  —  r,  side  M 

K  =  R  —  r  then 

R  —  r 

R+a  —  r  = J-. 

'  cos  0 

.           J      J     •        r>      ^+  cosB{a—r) 
Transposmg  and  reducmg,  R  = iZT^Jq * 

MI  —  D  J57  distance  to  move  back  on  tangent  in  flattening  curve  =  (R 
—  r)  tan  fi.        .  A  B.  &  O.  Engineer. 


STAKING  OUT  SWITCHES.  95 

STAKING    OUT   SWITCHES. 

BY  J.  F,  LE  BARON,  C  E. 

The  first  thing  is  to  find  the  radius  R  of  the  center  line  of  the  turnout 
curve.    To  find  this  we  must  have  the  following  data  : 

The  gauge  of  the  track  =  g. 

The  "throw  "of  the  switch  rail  =  d,  which  is  generally  taken  as  5 
inches. 

The  angle  which  the  switch  rail  makes  with  the  main  track  =S,  which 
varies,  of  course,  with  the  length  of  the  rail.  The  length  varies  from  18 
to  30  ft. 

The  frog  angle  =  F. 

The  radius  R  of  the  center  line  of  the  turnout  is  then  found  by  Henck's 
formula,  adapted  to  logarithms  : 

RJ-Xn=  i<9  —  d) 

■^  ^^      sin.  i(F+S)  sin.  i(F—  S) ' 
From  this  we  have  R  by  subtracting  the  value  of  ig. 
We  now  proceed  to  compute  the  position  of  the  point  of  the  frog,  which 
is  located  in  reference  to  the  throw  or  mouth  end  of  the  switch  rail. 

Referring  to  the  figure,  we  will  call  the  distance  from  the  mouth  of  the 
switch  to  the  point  of  the  frog  B  F. 

Then  BF  by  Henck's  formula  =    .     ^.  ~  ^ — --,  • 
^  sin.  i{F  +  i>) 

We  are  now  ready  to  stake  out  the  switch  or  turnout.  Two  cases  may 
occur : 

1st.  The  location  of  the  switch  throw  may  be  fixed. 

2d.  The  location  of  the  frog  in  the  track  may  be  fixed. 

In  the  first  case  the  position  of  the  switch  throw  being  fixed,  we  will 
drive  a  hub  with  nail  in  the  center  (x)  of  the  proposed  turnout  opposite 
the  switch  throw,  determining  its  position  by  measuring  from  the  rail  one- 
half  the  gauge  of  the  track  plus  the  throw  of  the  switch,  which  last  we 
Will  consider  to  be  5  ins  Tneoretically,  this  should  be  measured  at  right 
angles  to  the  position  of  the  switch  rail  in  the  _^  ^ 
turnout ;  but,  practically,  it  can  be  measured 
at  right  angles  to  the  rails  of  the  main  track. 
Mark  a  point  (D)  on  the  inside  of  the  rail  of 
the  main  track  opposite  this  for  the  end  of  the 
switch  rail,  and  measure  back  on  the  iron  the 
length  chosen  for  the  switch  rail,  and  mark  a 
point  (A)  on  the  inside  of  the  rail  for  the  heel  of  the  switch  rail.  The 
length  of  the  switch  rail  is  generally  20  or  22  ft.,  but  this  may  be  varied  to 


96  TOPOGRAPHY  AND  STAKING-OUT  PROBLEMS. 

save  cutting  the  iron.  Short  switch  rails  are  more  easily  worked  and  are 
safer,  but  less  than  18  ft.  is  objectionable,  as  not  apt  to  make  a  smooth 
running  curve  and  liable  to  jar  the  train.  We  now  measure  off  the  chord 
(BF),  which  we  have  previously  found  by  computation  from  the  throat 
of  the  switch,  and  .42  of  afoot  from  the  inside  of  the  rail  of  the  main 
track,  swinging  in  the  dist.  {BF)  to  such  a  point  (F)  as  it  will  touch  the 
inside  edge  of  the  rail  of  the  main  track.  This  gives  the  position  of  the 
point  of  the  frog  in  the  track,  which  we  mark  on  the  rail. 

The  section  master  will  set  the  frog  in  the  track  at  this  point  without 
further  marking. 

We  now  set  up  the  transit  on  the  hub  at  x  and  lay  off  the  curve  of  the 
turnout—  the  radius  of  which  we  have  already  computed — by  setting 
stakes  in  the  center  line  every  12rlt  ft.,  using  a  parallel  to  the  switch  rail 
in  its  position  in  the  turnout,  for  tangent  and  deflecting  as  iisual. 

We  know  the  radius  of  the  turnout,  and  we  can  consequently  compute 
the  ordinate  for  bending  the  rails  by  the  formula  on  page  14  of  Henck, 

m  =  — ,  in  which  m  equals  the  ordinate  required  in  decimals  of  a  foot, 

2R 
and  I  equals  the  length  of  the  rail  used.    It  can  also  be  taken  from  Table 
I.  {ibid). 

The  angle  S  which  the  switch  rail  makes  with  main  track  is  easily 
computed,  as  we  know  or  assume  the  length  of  the  switch  rail  and  the 

d 
throw  of  the  same,  and  therefore  sin.  S  =  — . 

I 

The  frog  angle  F  is  known  or  easily  found  by  measuring  the  frog,  and 
computing,  or  by  taking  a  paper  pattern  of  the  point  angle  and  applying 
a  protractor. 

In  the  second  case,  where  the  point  of  the  frog  is  fixed  in  the  main 
track,  we  have  to  locate  the  switch  throw  from  this  point  by  measuring 
back  the  chord  BF  to  a  point  B,  0.42  ft.  from  the  main  track  rail. 

In  the  case  of  a  switch  with  a  double  throw,  where  two  turnouts  leave 
the  main  track  from  the  same  point,  it  is  well  to  paint  the  stakes  of  each 
turnout  a  different  color,  to  avoid  confusing  the  trackmen. 

We  have  supposed  the  main  track  to  be  on  a  straight  line.  If  the  turn- 
out is  from  a  curve  the  problem  is  more  complicated,  but  it  can  easily  be 
solved  by  prob.  57,  page  38,  Henck. 

As  a  check  upon  the  somewhat  long  computation  required  when  the 
turnout  is  from  the  inside  of  a  curve  I  have  sometimes  adopted  the  fol- 


STAKING  OUT  SWITCHES.  97 

lowing  mechanical  method  of  obtaining  the  position  of  the  point  of  the 
frog  and  the  frog  angle  : 

I  set  up  the  transit  on  the  switch  throw  at  B  and  lay  out  the  outer  rail 
of  the  turnout  by  deflection  angles  to  any  assumed  radius,  finding  the 
point  of  the  frog  by  repeated  trials  of  deflection,  and  then  measuring  the 
frog  angle  by  means  of  a  lieht  board  with  a  nail  driven  through  it  at  the 
point  of  the  frog.  This  nail  in  the  board  is  set  over  the  point  of  the  frog 
when  found,  and  a  pattern  of  the  frog  angle  made  on  it  by  means  of  de- 
flections with  the  transit,  to  establish  the  curve  on  the  board.  From  this 
curve  the  tangent  T  at  i^  is  laid  off  and  the  frog  angles  measured  with  a 
protractor,  or  otherwise. 

This  method  uses  the  rad.  for  the  outer  rail  only,  and  saves  computa- 
tion for  the  frog  angle  and  position. 

The  method  I  have  described  makes  the  turnout  curves  tangent  to  the 
switch  rail,  and  consequently  compounds  the  curve  from  B  to  A.  This 
is  no  practical  detriment,  for  generally  the  diflference  in  radius  is  very 
slight,  between  the  radius  of  the  switch  rail  and  the  rest  of  the  turnout, 
which  is  more  than  overcome  by  the  manipulations  of  the  trackmen. 

Some  engineers,  however,  prefer  to  make  the  curve  tangent  at  the  heel 
of  the  switch  rail  A.  In  that  case  the  throw  of  the  switch  rail  must 
sometimes  be  slightly  changed  (only  a  slight  change  is  admissible  with 
ordinary  iron)  or  the  length  of  the  switch  rail  must  be  changed.  But  for 
safety  in  traflic  the  length  of  the  switch  rail  should  not  be  much  in- 
creased, and  if  diminished  nothing  is  gained. — Engineering  News,  Sept. 
9,  1892. 


98  TOPOGRAPHY,  AND  STAKIN(J-OUT  PROBLEMS. 


METRIC  RAILWAY  CURVES. 
[Fom  Engineering  News,  Oct.  13, 1883.] 


Several  inquiries  have  appeared  from  time  to  time  in  Engineerinq 
News  for  a  metric  table  of  railway  curves.  We  to-day  present  one  pre 
pared  by  an  engineer  who,  after  practicing  the  American  method  of  lay- 
ing out  curves  in  the  United  States,  has  been  for  two  years  occupied  ia 
railroad  surveying  with  the  metric  system  in  Mexico. 

The  table  is  explained  by  the  headings  of  the  columns.  Curves  are 
designated  (as  in  the  first  column)  by  the  angle  which,  according  to  the 
American  system,  has  to  be  turned  off  repeatedly  at  a  point  on  the  cir- 
cumference, and  is  subtended  by  successive  equal  choi-ds.  This  angle  is 
called  by  Trautwine  and  Shunk  the  "  tangential "  angle  ;  by  Henck  and 
Searles  the  "deflection"  angle.  In  the  first  article  of  the  appendix  to  his 
revised  edition,  Prof.  Henck  suggests  the  use  of  this  angle  for  designat- 
ing curves  run  by  the  metric  system.  An  obvious  advantage  thus  gained 
is  that  the  angle  to  be  measured  in  staking  jut  a  curve  in  a  field  is  simply 
the  angle  named  in  speaking  of  the  curve.  The  equal  chords  successively 
measured  according  to  the  metric  system  should  be  20  meters  in  length, 
as  was  abundantly  enforced  by  numerous  writers  who  discussed  the  point 
in  Engineering  News  a  year  and  a  half  ago.  As  to  the  adaptability  of 
that  length  to  railroad  engineering,  it  may  be  noticed  that  in  the  first  e:i- 
ample  of  staking  out  a  curve  given  in  Shunk's  "Field  Engineer,"  the 
length  of  chord  is  taken  to  be  20.12  m.,  which  be  calls  66  feet.  The 
stakes,  set  at  successive  20-meter  intervals,  are  to  be  marked  with  the  suc- 
cessive even  numbers,  2,  4,  6,  8,  etc.,  so  as  to  constitute  the  dekameter  the 
unit  of  stake  numbering.  Each  stake  is  thus  designated  by  its  distance 
in  dekameters  from  the  zero  point,  and  each  kilometer  stake  is  marked 
by  an  exact  hundred.  The  an^le  by  which  the  curve  changes  its  direc- 
tion per  unit  of  length  as  thus  marked  is,  therefore,  one-half  of  its 
change  of  direction  between  the  extremities  of  the  20-meter  chord ; 
that  is,  it  is  exactly  the  "  20-meter  chord  "  angle  used  to  stake  it  out  and 
to  designate  it;  and  the  total  change  of  direction  made  by  any  length  of 
the  curve  is  simply  the  product  of  this  angle  multiplied  by  the  difference 


METRIC  RA.ILWAY  CURVES.  99 

in  the  numbers  of  the  stakes  at  its  beginning  and  end,  just  as  in  the  pres- 
ent practice  in  the  United  States, 

For  convenience  in  staking  fractional  parts  of  the  20-meter  chain,  the 
second  column  of  the  table  is  given,  showing  the  number  of  minutes  to 
be  turned  off  with  the  transit  per  meter,  being  simply  one-twentieth  of 
the  angle  in  the  fir-- 1  column.  Here  a  slight  advantage  over  the  lOO-ft* 
chord  is  seen,  because  60  bears  a  simpler  relation  to  20  than  to  100, 

The  column  of  radii  presents  a  simplicity  superior  to  the  100-ft.  system, 
in  that  the  metric  radius  is  just  10  times  the  co-secant  of  the  angle  in  the 
first  column,  and  can  therefore  be  taken  directly  from  a  trigonometrical 
table  by  altering  the  decimal  point,  or  in  the  case  of  the  logarithm,  the 
characteristic.  The  computation  in  the  present  United  States  practice  is 
a  little  more  complicated.  The  dfference  thereby  produced  in  the  figures 
may  be  seen  by  comparing  the  columns  of  20-meter  chord  angle  and 
radius  with  the  columns  of  degree  of  curve  and  radius  in  the  field-books 
commonly  used  in  this  country.  Tlie  metric  radii,  instead  of  being  fig- 
ured exactly  one-tenth  of  the  expression  in  feet  corresponding  to  the 
same  angle,  have  slightly  larger  decimals.  The  discrepancy  is  so  small, 
however,  that  for  the  greater  part  of  railroad  work  the  old  tables  might 
be  used  with  the  metric  system,  by  taking  the  old  degrees  for  the  20-meter 
chord  angles  and  dividing  all  the  old  radii  by  10,  that  is,  merely  changing 
the  decimal  point  one  place.  It  is  different  with  the  figures  for  deflection 
distances  and  ordinates,  which,  in  the  metric  table,  are  almost  exactly 
four-tenths  of  what  they  are  in  the  old  tables  for  the  same  angle  in  first 
column, 

Tlie  precise  length  of  the  curve,  in  contradistinction  to  that  of  the  chords 
by  which  it  is  staked  out,  is  seldom  required.  The  last  column  in  the 
table  is  inserted  chiefly  with  a  view  to  exhibiting  the  percentage  to  be 
added  to  such  a  chord  to  get  the  length  of  arc  it  subtends.  This  percent- 
age IS  clearly  seen  when  we  move  tlie  decimal  point  of  the  last  column 
one  place  to  the  left;  and  it  may  be  made  useful  in  connection  with  such 
tables  as  are  given  at  the  end  of  Shunk's  "  Field  Engineer"  and  of  the  re- 
vised edition  of  Henck's  "  Field  Book."  For  example,  those  tables  give, 
among  other  very  useful  data,  the  distance  from  the  intersection  point  to 
either  extremity  of  a  one-degree  curve  whose  total  length  varies  between 
0°  and  90°.  Mr.  Shunk  calls  this  the  "apex  distance  ;"  Prof.  Henck,  the 
"tangent."  For  a  curve  90' in  length,  Mr.  Shunk's  table  gives  5730  ft. 
Prof.  Henck's,  5729.7  ft.,  the  same,  of  course,  as  the  radius.  Either  of 
these  divided  by  10  can  be  used  in  practice  for  the  metric  1°  curve,  whose 


100 


TOPOGRAPHY.  AND  STAKING-OUT  PROBLEMS. 


•3    . 

Quarter 

I  ca  .•  t. 

K 

ct 

Middle. 

point. 

< 

h 

Deflection. 



- 

Q 

-J 
IS. 

0^' 

"S 

Ordinate 

§ 

Radius 

IN 

METEBS 

3437.75 

a 

■Cm 

at  distance 
from  end-chord. 

n  PS -a  « 

o 

From 
tan- 
gent. 

From 
chord. 

■  H 

Of  10 
m. 

Of  5  m. 

"ooic 

3.5362745 

.058 

.116 

.Olo 

.011 

10.0000 

20' 

1' 

1718.38  3.2352463 

.116 

.233 

.029 

.022 

10.0001 

30' 

1^' 

1145.93  3.0591581 

.175 

.349 

.044 

.033 

lO.OOOJ 

40' 

2' 

859.462.9342237 

.233 

.465 

.058 

.044 

10.0002 

50' 

2}i' 

687.57  2.8373192 

.291 

.582 

.073 

.055 

10.0004 

!•    0' 

3' 

572.99  2.7581447 

.349 

.698 

.087 

,065 

10.0005 

10' 

3ii' 

491.14  2.6912059 

.407 

.814 

.102 

.076 

10.0007 

20' 

4' 

429,76  2.6332231 

.465 

.931 

.116 

.087 

10.0.00 

30' 

4JlS' 

382.02 

2.5820810 

.524 

1.047 

.131 

.098 

10.0011 

40' 

5^ 

343.82 

2.5363351 

.582 

1.163 

.145 

.109 

10.0014 

50' 

5>i' 

312.58 

2.4949553 

.640 

1.28U 

.160 

.120 

10.0017 

2*    0' 

6' 

286.54 

2.4571808 

.698 

1.396 

.175 

.131 

10.0020 

10' 

6H' 

264.51 12.4224340 

.756 

1.512 

.189 

.142 

10.0024 

20' 

7' 

245.62  2.3902659 

.814 

1.629 

.204 

.153 

10.0028 

30' 

7^' 

229.26  2.3603204 

.873 

1.745 

.218 

.164 

10.0032- 

40' 

8' 

214.94  2.3323107 

.931 

1.861 

.233 

.175 

10.0036 

50' 

8Ji' 

202.30  2.3060020 

.989 

1.977 

.247 

.186 

10.0041 

8*    0' 

9' 

191.07  2.2811998 

1.047 

2.093 

.262 

.196 

10.0046 

10' 

9H' 

181.0312.2577414 

1.105 

2.210 

.276 

.207 

10.00.51 

20' 

10' 

171.9812.2354889 

1.163 

2..326 

.291 

.218 

10.0056 

30' 

10^' 

163.80  2.2143247 

1.222 

2.442 

.306 

.229 

10.0062 

40' 

11' 

156.37  2.1941477 

1.280 

2.558 

.320 

.240 

10.0068 

50' 

n^' 

149.58  2.1748701 

1.338 

2.674 

.335 

.251 

10.0075 

4°    0' 

12' 

143.36  2.1564155 

1.396 

2  790 

.349 

.262 

10.0081 

10' 

1%' 

137.63  2.1387167 

1.454 

2.9t,6 

.364 

.273 

10.0088 

20' 

13^ 

132.35  2.1217146 

1.512 

.3.022 

.378 

.284 

10.0095 

30' 

1314' 

127.45  2  1053567 

1.570 

3.138 

.393 

.295 

10.0103 

40' 

14' 

122.91 

2.0895961 

1.629 

3.254 

.407 

..306 

10.0111 

50' 

14^' 

118.68 

2.0743911 

1.687 

3.370 

.422 

.317 

10.0119 

fi"    0' 

15' 

114.74'2.0597040 

1.745 

3.486 

.437 

.328 

10.0127 

20' 

16' 

107.5812.0317513 

1.861 

3.718 

.466 

.349 

10.0145 

40' 

17' 

101.28  2.0055032 

1.977 

3.950 

.495 

.371 

10.0163 

6°    0' 

18' 

95.67  1.9807654 

2.093 

4.181 

.524 

.393 

100183 

20' 

ID' 

90.65  1.95737511 

2.210 

4.413 

.553 

.415 

10.0204 

40' 

20' 

86.14 

1.9351943 

2.326 

4.644 

.582 

.437 

10.0226 

T    0' 

21' 

82.06 

1.91410.55 

2.442 

4.875 

.612 

.459 

10.0249 

20' 

22' 

78.34  1.89400761 

2  558 

5.106 

.641 

.481 

10.0274 

40' 

23' 

74.96:1.8748128 

2.674 

6.336 

.670 

.503 

10.0299 

8"    0' 

24' 

71.8511.8564447 

2.790 

5.567 

.699 

.525 

10.0326 

20' 

25' 

69.00  1.8388361 

2.906 

5.797 

.729 

.547 

10.0353 

40' 

26' 

66.36  1.8219279 

3.022 

6.027 

.758 

.569 

10.0382 

9"    0' 

27' 

63.92  1.8056676 

3.138 

6.257 

.787 

.591 

100412 

20' 

28' 

61.66  1.7900083 

3.254 

6.487 

.816 

.613 

10.0444 

40' 

29' 

59.55  1.7749082 

3.370 

6.7i7 

.846 

.635 

10.0476 

10°    0' 

30' 

57.591.7603298 

3.486 

6.946 

.875 

.657 

10.0510 

METRIC  RAILWAY  CURVES.  101 

radius  is  573.99.  (It  would  be  still  better  in  using  the  metric  system  to 
have  a  new  table  calculated  expressly  for  radius  573.958.)  To  get  with 
very  close  approximation  the  coiTesponding  dimensions  for  any  other 
curve  we  divide  by  the  degree  designating  the  curve.  Hence,  for  a  90° 
length  of  a  metric  10'  curve  we  should  get  a  tangent  or  apex  distance  of 
57.30  m.  In  the  case  of  so  sharp  a  curve  tlie  question  arises  whether  this 
is  sufficiently  accurate  for  our  purpose,  and  this  question  is  answered  by 
reference  to  the  last  column  in  the  metric  table.  After  moving  the  deci- 
mal point  as  above  directed,  we  find  1.0051  for  the  10°  curve,  showing  that 
our  57.30  is  in  error  by  one-half  of  one  per  cent.  To  get  exactly  the  dis- 
tance required,  multiply  5730  by  1.005,  and  we  get  57.59,  just  as  given  in 
the  metric  table  for  the  radius  of  the  10°  curve.  The  same  percentage 
correction  is  applicable  to  the  other  tabulated  data  as  well  as  to  the  tan- 
gent or  apex  distance. 

In  computations  like  that  discussed  in  the  preceding  paragraph,  the  20- 
meter  chord  has  the  advantage  over  that  of  100  ft.  that  it  is  a  shorter 
length,  and  consequently  the  arc  it  subtends  in  any  circle  differs  by  a 
smaller  percentage  from  the  chord.  Hence,  the  tabulated  data  above 
mentioned  can  be  applied  without  requiring  correction  to  a  larger  range 
of  metric  curves  than  of  the  curves  used  in  the  American  foot  practice. 
For  example,  observe  that  in  the  curves  of  b6.14  and  90.65  meters  radius 
the  percentage  is  less  than  one-quarter  of  one  per  cent.  Between  the  two 
lies  the  20°  curve,  as  given  in  the  Ame  rican  tables,  with  a  radius  of  287.9 
ft.,  in  which  the  100-ft.  chord  subtends  an  arc  of  100.5  ft.,  shovsing  a  per- 
centage of  one-half  of  one  percent.  Accordingly,  if  we  start  5,730  ft., 
the  tabulated  tangent  or  apex  distance  above  cited  for  90°  length  of  an 
American  1"  curve,  and  take  one-twentieth  of  it  for  the  corresponding 
dimension  of  thetcircle  of  287.9  ft.,  radius,  we  have  286,5  ft.,  and  must 
add  1.4  ft.  to  get  the  correct  value  equal  to  radius.  On  the  other  hand, 
suppose  we  had  started  with  573  mefc.-s  as  the  tangent  or  apex  distance 
in  the  metric  1'  curve,  to  get  the  corresponding  dimension  of  the  circle  of 
86.14  meters  radius  observe  that  that  circle  is  designated  by  the  20  m. 
chord  angle  of  6|  ;  three-twentieths  of  573  m.  is  85.95  m.,  and  to  get  the 
correct  value  equal  to  radius  we  must  add  0.19  m.,  which  is  lees  than  half 
of  1.4  ft.,  and  less  than  one  quarter  of  one  per  cent. 

Engineers  accustomed  to  tliinking  of  curves  by  their  American  desig- 
nations may  find  it  convenient  in  making  mental  comparisons  to  bear  in 
mind  that  if  any  curve  has  its  20-m.  chord  angle  multiplied  by  3,  the  pro- 
duct is  nearly  the  "  degree"  used  to  designate  the  curve  in  this  country; 


l02  TOPOGRAPHY,  AND  STAKING-OUT  PROBLEMS. 

for  100  ft.  is  very  little  more  than  3  dekameters.  For  instance,  the  curve 
last  spoken  of,  having  a  radius  of  86.14  m.  and  designated  by  the  angle 
of  6f  ,  is  almost  the  same  as  the  American  curve  of  20%  or  3  X  6|°.  The 
number  of  20  is  given  in  the  metric  table  in  the  column  of  minutes  to  be 
laid  off  per  meter  in  staking  out,  as  belonging  to  the  curve  of  86.14  m. 
radius;  and  all  of  the  numbers  in  that  column,  instead  of  being  read  as 
minutes,  might  be  regarded  as  the  "degrees"  designating  American 
curves,  in  which  case  the  corresponding  iigures  of  radii  would  be  nearly 
the  true  value  of  meters  of  the  radii  of  those  American  curves. 


CHAPTER  V. 


Transition  or  Easement  Curves. 

Professor  Arthur  N.  Talbot,  of  the  University  of  Ilhnois,  Champaign, 
111.,  has  published  a  valuable  paper  on  easement  curves  in  TheTechnograph, 
1890-91,  from  which  we  quote  as  follows  : 

THE  TAPERING  CURVE. 

The  Tapering  Curve  is  a  compound  curve  consisting  of  a  series  of  cir- 
cular curves  of  the  same  length,  whose  degree-of -curve  increases  by  some 
constant  difference  up  to  the  degree  of  the  main  curve.  Thus,  if  the 
taper  is  1"  for  each  30  feet,  the  approach  from  a  tangent  to  a  6°  curve 
will  be  made  by  30  feet  of  1°  curve,  30  feet  of  2°  curve,  30  feet  of  3°  curve, 
30  feet  of  4°  curve,  and  30  feet  of  5'  curve,  after  which  the  6°  curve  is 
run  in. 

If  the  degree  of  the  main  curxe  is  not  a  multiple  of  the  common  dif- 
ference of  the  tapers,  at  the  end  of  the  last  full  chord  a  fractional  chord 
is  used,  proportional  to  the  diflFerence  of  the  degree  of  the  main  curve  and 
last  taper.  Thus,  for  a  taper  of  2°  30'  per  30  feet,  an  8°  curve  would  be 
reached  by  30  feet  of  2°  30'  and  30  feec  of  5°  curve,  ending  with  6  feet  of 
7°  30'  curve;  since  8"  is  in  excess  of  7°  30'  by  one-fifth  of  the  change  2°-30', 
one- fifth  of  a  full  chord  is  used. 

In  order  to  run  the  curve  with  the  transit  at  the  beginning  of  the  taper- 
ing curve  or  at  some  corresponding  point— thus  saving  settling  at  each  P. 
C.  C. — a  table  giving  deflection  angles  to  the  different  P.  C.  C.'s  is  used. 

The  tapering  curve  was  introduced  by  Mr.  William  Hood,  Chief  En- 
gineer of  the  Southern  Pacific  Railway,  and  has  been  extensively  used 
on  the  Southern  Pacific,  Northern  Pacific,  Missouri  Pacific,  and  other 
western  roads.  It  makes  a  good  transition  curve,  and  does  not  vary 
much  from  the  transition  spiral.  However,  it  lacks  flexibility,  this 
property  being  secured  only  by  a  wide  range  of  tapers,  necessitating 
many  tables. 


104  TRANSITION  OR  EASEMENT  CURVES, 

THE  EAILROAD  SPIRAL. 

Th§  Railroad  Spiral,  as  developed  by  Wm.  H.  Searles,  C.  "E.,  is  a  multi- 
form compound  curve,  differing  from  the  tapering  curve  by  using  the 
central  angles  of  the  successive  arcs  as  constant  quantities,  and  varying 
the  length  of  arc  or  chord  to  secure  different  spirals.  The  first  arc  has 
10'  central  angle,  the  second  20',  the  third  30',  and  so  on  to  the  end  of  the 
transition  curve.  Mr.  Searles  has  published  a  little  hand-book  of  tables 
and  explanations  for  this  curve.  Tables  of  deflection  angles  with  the 
transit  at  any  chord  point  are  given.  These  deflections  are  constant  what- 
ever the  chord  length.  Thus,  the  deflection  to  the  end  of  the  8th  chord  is 
2°  07',  whether  the  length  of  curve  be  8  X  10  feet  or  8  X  21  feet,  and  the 
central  angle  subtended  will  also  be  the  same.  However,  the  degree-of- 
curve  of  the  arcs  will  vary  with  a  change  in  length  of  chord.  This  ne- 
cessitates a  set  of  tables  giving  the  degree-of -curve  for  the  last  chord  in 
the  curve.  As  this  is  not  an  integral  number,  the  one  nearest  the  degree 
of  the  main  curve  is  chosen.  This  is  allowable,  since  it  consists  in  com- 
pounding the  last  arc  with  the  main  cui  ve.  As  several  chord  lengths  with 
the  corresponding  number  of  chords  will  give  about  the  same  degree-of- 
curve,  a  variety  of  spirals  for  any  main  curve  is  secured.  About  sixty 
tables  are  given  in  Searles'  "  The  Railroad  Spiral,"  to  which  the  student  is 
referred  for  further  information. 

The  "  railroad  spiral "  approaches  very  near  the  true  transition  spiral. 
With  the  tables  given,  the  calculations  and  field  work  are  simple  and 
rapid.  Deflections  for  points  between  the  chord  points  are  found  by  in- 
terp)o]ating  in  the  tables,  but  only  chord  points  may  be  used  as  transit- 
points.  An  objection  has  been  made  that  the  degree-of-curve  for  any 
chord  is  not  an  integral  midtiple  of  the  number  of  the  chord.  This,  how- 
ever, is  not  of  great  importance. 

THE  PENNSYLVANIA  METHOD. 

The  Pennsylvania  Railroad  uses  200  ft.  of  30'  curve  at  the  ends  of  a  simple 
curve.  For  sharp  curves  100  ft.  of  1  curve  is  put  in  at  either  end.  The 
super-elevation  begins  with  zero  at  the  P.  C,  and  increases  uniformly 
to  the  full  amount  at  the  beginning  of  the  main  curve.  The  claim  is 
made  that  in  this  manner  the  complete  super-elevation  is  attained 
while  the  car  is  on  a  light  curve  where  the  wheels  keep  to  the  outer  rail, 
and  that  the  shock  incident  to  gaining  the  super-elevation  while  on  the 
tangent  is  avoided.  Of  course  the  field  work  is  simple.  It  is  claimed 
that  this  method  is  very  efficient,  but  it  is  open  to  criticism. 


THE  TRANSITION  SPIRAL.  105 

THE  TRANSITION  SPIRAL. 

The  Transition  Spiral  is  a  curve  whose  degree-of-curve  increases  directly 
as  the  distance  along  the  curve  from  the  point  of  curvature. 

Thus,  if  the  spiral  is  to  change  at  the  rate  of  10°  per  100  feet,  at  10  feet 
from  the  beginning  of  the  spiral  the  curvature  will  be  the  same  as  that  of 
a  1°  curve;  at  25  feet,  as  of  a  2°  30'  curve;  at  60  feet,  as  of  a  6°  curve.  Like- 
wise, at  60  feet,  the  spiral  may  be  compounded  with  a  6°  curve;  at  80  feet, 
with  an  8'  curve,  etc. 

This  curve  fulfills  the  requirements  for  a  transition  curve.  Its  curva- 
ture increases  at  the  distance  measured  around  the  curve.  The  formulas 
for  its  use  are  comparatively  simple  and  easy.  The  field  work  and  the 
computations  necessary  in  laying  it  out  and  connecting  it  with  circular 
curves  are  neither  long  nor  complicated,  and  are  similar  to  those  for  sim- 
ple circular  curves.  The  curve  is  extremely  flexible,  and  may  easily  be 
adapted  to  the  requirements  of  varied  problems.  The  rate  of  change  of 
degree-of-curve  may  be  made  any  desirable  amount  according  to  the  max- 
imum curve  used,  or  according  to  the  requirements  of  the  ground. 

[For  the  formulas  and  tables  deduced  by  Professor  Talbot  for  the  transi- 
tion spiral  we  refer  to  the  Tedinograph,  1890-91.] 

When  simple  curves  are  left  without  transition  curves,  many  track-men 
•'ease"  the  curve  by  throwing  the  P.  C.  inward  a  short  distance  and 
gradually  approaching  the  tangent  a  few  rail-lengths  away,  while  the 
main  curve  is  reached  finally  by  sharpening  the  curve  for  a  short  dis- 
tance.   Even  this  is  better  than  no  easement -curve. 

The  objection  is  sometimes  raised  that  even  if  track  is  laid  out  with  a 
carefully  fitted  spiral  there  would  be  no  possibility  of  keeping  it  in  place 
by  the  methods  of  the  ordinary  track-man.  This  identical  objection  could 
be  made  with  the  same  force  against  carefully  laid  out  circular  curves, 
yet  no  engineer  would  recommend  abolishing  that  practice.  Even  if,  in 
re-lining,  the  transition  curve  is  considerably  distorted,  it  remains  an 
easement,  and  will  be  in  far  better  riding  condition  than  a  distorted 
circular  curve.  By  marking  the  P.  S.  and  the  P.  C.  C.  with  a  stake  or 
post,  with  possibly  on  long  spirals  an  intermediate  point,  the  track-man 
will  be  able  to  keep  the  spiral  in  as  good  condition  as  though  it  were  of 
uniform  curvature. 

Properly  constructed  spirals  would  frequently  allow  the  use  of  sharper 
curvature— since  the  riding  quality  of  curves  may  be  the  governing  con- 
sideration in  the  selection  of  a  miximum — and  thus  make  a  savins' m 
construction.    By  fitting  curves  with  proper  transition  spirals,  roads 


106 


TRANSITION  OR  EASEMENT  CURVES. 


using  sharp  curves  may  partially  relieve  the  objection  of  the  public  to 
traveling  by  their  routes.  The  transition  curve  has,  then,  a  financial 
value  largely  overbalancing  its  cost.  The  adoption  of  such  curves  by 
many  of  our  principal  railways  proves  their  efficiency,  and  the  future  will 
see  a  much  more  general  adoption. 

LOCATION  OF  THE  CUBIC  PARABOLA. 
By  Professor  Fred  P.  Sj.  aiding,  Cornell  University. 

The  necessity  for  using  some  form  of  easement  curve,  to  connect  the 
circular  arcs  upon  railroad  lines  with  the  tangents,  is  now  very  generally 
recognized.  Their  adoption,  however,  has  been  greatly  retarded  by  the 
difficulty  met  in  attempting  to  reduce  a  satisfactory  curve  to  a  convenient 
form  for  ready  use  in  the  field. 

Two  methods  of  location  are  at  present  in  use  ;  first,  by  Froude's  for- 
mulas for  the  cubic  parabola  as  given  by  Rankine,  the  determination  of 
the  ordinates  for  setting  out  being  mide  for  each  curve  directly  from  the 
formulas  ;  and  second,  the  method  of  the  railroad  spiral  as  given  by 
Searles  and  others,  in  which  practically  the  sime  curve  is  located  by 
means  of  deflection  angles  corresponding  to  various  fixed  chord  lengths, 
the  curve  beuig  varied  by  changing  the  chord  length. 

The  object  of  this  paper  is  to  show  how  by  a  simple  tabulation  an  ap- 
proximation to  the  cubic  parabola  may  be  readily  located  in  practice, 
either  by  ordinates  or  deflection  angles,  without  the  necessity  of  makinjr 
calculations  from  formulas  for  each  case,  but  at  the  same  time  allowing  the 
use  of  chords  of  any  lengths  and  the  placing  of  stations  wherever  desired. 

The  formulas  for  this  curve  as  given  by  Rankine  are 


y 


4  8  a^ 


<1)  a°d  s  =  ^  (2) 


in  which  s  is  the  shift  or  offset  B  C  (Fig.  1)  of  the  circular  arc  from  the 

tangent,  I  is  the  length  AD 
(Fig.  1)  of  the  easement  curve. 


M- 


Fig.  I. 


R  is  the  radius  of  the  circular 
arc,  and  y  is  the  perpendicu- 
lar offset  from  the  tangent  or 
from  the  circular  arc  to  the 
easement  curve,  at  any  point 
distant  x  from  the  junction 
of  the  easement  curve  with 
the  tangent  or  circular  arc. 


LOCATION  BY  ORDINATKS.  107 

If  it  be  desired  to  connect  two  curves  of  different  degrees,  the  same  form 
of  easement  curve  may  be  employed,  using  only  the  portion  of  it  which 
lies  between  the  points  where  its  radius  of  curvature  equals  the  radii  of 
the  arcs  to  be  connected.  For  this  case,  equation  (1)  applies  directly, 
while  for  the  value  of  the  shift  (3)  becomes 
_  I-  (fli  —  -Rg) 

in  which  R^  and  R^  are  the  radii  of  the  circxilar  curves. 

LOCATION  BY  ORDINATES. 

In  order  to  locate  an  easement  curve  by  this  method,  it  is  necessary  to 
assume  the  value  of  either  the  length  or  the  shift  and  calculate  the  other 
from  formula  (3)  or  (3).  The  shift  may  be  fixed  by  topographical  con- 
siderations, or  the  length  may  be  determined  by  fixing  the  value  for  the 
ratio  of  the  change  in  i-ail  elevation  to  the  length,  authorities  differing  as 
to  the  best  value  to  use  for  this  ratio,  but  probably  any  value  above  the  1 
m  300  recommended  by  Froude  will  give  goo  i  results.  Having  thus 
found  the  value  for  the  shift,  it  is  to  be  laid  off  from  the  tangent  toward 
the  center  of  the  proposed  curve,  and  the  circular  arc  run  in  from  a 
parallel  tangent  at  that  distance  from  the  main  one.  In  other  words,  in 
locating  a  line  upon  which  easement  curves  are  to  be  used,  the  circular 
curves,  instead  of  being  placed  in  the  usual  manner  tangent  to  the  straight 
portions  of  the  track,  should  be  made  tangent  to  parallel  lines  at  a  distance 
s  from  the  main  tangents,  and  in  the  same  way  the  arcs  of  a  compound 
curve  should  not  be  tangent  to  each  other  at  the  P.  C.  C,  but  the  arc  of 
smaller  radius  should  begin  at  a  point  on  the  common  radial  line  distant 
s  inward  from  the  end  of  the  larger  arc. 

The  half-length  of  the  easement  curve  is  then  laid  off  from  the  P.  C.  on 

the  circular  arc,  and  the  point  D  (Fig.  1)  so  found  will  be  the  junction  of 

the  two  curves  ;  the  half-length  is  also  laid  off  on  the  main  tangent  from 

a  point  opposite  the  P.  C.  (B,  Fig.  1)  to  find  the  point  of  tangency  A  (Fig. 

1 )  of  thp  easement  curve. 

I 
Having  determined  these  poinls,  different  values  of  x  less  than   -  sub- 

stituted  in  formula  (1)  will  give  values  of  y  to  be  laid  off  from' points  dis 
tant  X  from  D  on  the  circle,  and  from  A  on  the  tangent,  to  determine 
points  on  the  easement  curve. 

Tables  may  now  be  constructed  on  these  formulas  which  will  give  di- 
rectly the  value  of  the  ocdinates  to  be  used  in  placing  the  curve  on  the 
ground,  and  as  experience  has  shown  that  comparatively  few  variations 


108  TRANSITION  OR  EASEMENT  CURVES. 

will  be  necessary  to  meet  all  cases  in  practice,  such  tables  need  not  be  very 
extended  to  answer  all  requirements. 

In  order  to  construct  such  a  table,  suppose  that  the  curvature  is  to  in- 
crease r  for  every  50/^.  of  distance,  then  for  a  10°  curve.  I  =  500  ft.  and 

s  —  -r-^  =  18.16  ft;  substituting  these  values  in  (1),  if  x  =  10  ft.,  y  =: 

.0005H1  ft.    To  find  other  values  of  y  corresponding  to  different  values  of 

x,  we  notice  that  y  varies  as  the  cube  of  x,  and  thus  construct  the  last 

column  of  Table  1. 

In  order  to  extend  the  table  to  other  curves  in  which  the  curvature 

varies  differently,  we  notice  that,  combining  formulas  (1)  and  (3),  y  varies 

R 
as  -j  for  X  constant,  or,  approximately,  inversely  as  the  ratio  between 

length  and  curvature. 

In  the  table,  the  offset  is  given  for  every  10  ft.  of  length.  Intermediate 
values  may  be  found  by  interpolation,  without  sensible  error. 

To  illustrate  the  use  of  the  table  in  locating  a  curve,  suppose  that  two 
tangents  are  to  be  connected  by  a  compound  curve  composed  of  an  arc  of 
5°  and  one  of  8°  curvature,  and  that  the  changes  of  radius  are  to  be  eased 
by  curves,  in  which  the  curvature  increases  1°  for  every  AOft.  of  distance 
from  the  tangent. 

First  the  circular  curves  must  be  located  as  shown  by  the  full  lines 
(Fig.  1)  with  the  proper  shift  from  the  tangents  and  from  each  other. 

For  an  increase  of  curvature  of  1°  in  40  ft.,  the  length  of  easement 
curve  for  an  8°  will  be  320  ft. 

1  s 

When  X  =  —  (formula  1),  y  —  — ,  and  going  into  the  table  with  x 

2  2 

1  s 

=  —  =  160,  we  find  y  =  2.97  =  — ,  hence  B  C  =  s  =  5.94  ft.    In  the 

2  2 

same  way  ML  =  s  =  1.46  ft.  may  be  found  for  the  5°.  For  the  connec- 
tion between  the  two  circular  arcs,  I  =  the  difference  of  lengths  of  the 
curves  required  to  connect  the  two  arcs  with  tangent  =  320  —  200  —  120 

s 
ft.  and  as  before  —  =  .15  ft.  may  be  taken  from  the  table. 

2 

Now  to  locate  the  curve  AD,  suppose  that  the  P.O.  of  the  circular  arc 

comes  at  sta.  10  +  65  and  that  it  is  desired  to  mark  50  ft.  stations  on  the 

easement  curve,  these  stations  having  first  been  located  on  the  tangent 

AB  and  the  arc  CD.    As  the  half-length  of  the  easement  curve  is  160  ft. 


LOCATION  BY  DEFLECTION  ANGLB3.  109 

the  P.E.C.,  or  point  where  the  eauement  curve  leaves  the  tangent  will  be 
at  sta.  9  +  05.  The  quantities  necessary  to  lay  out  the  easement  curve 
may  then  be  tabulated  as  follows,  taking  values  of  y  to  nearest  tenth  foot. 

Sta.    9  +  05  P.  E.C.  X  =     0,  y  =  0.0,  Measured  from  tangent. 

9  +  50  x=   45,  y  =  0.1,  " 

10  x=   95,  y  =  0.6, 

10  +  50  a;  =  145,  y  =  2.2,  " 

10  + 65  P.C.      aj  =  160,  y  =  d.O, 

11  x  =  125,  y  =  2.4,  "  "     Curve  CD. 
11  +  50  x=   75,  y  =  0.3, 
13  x=   25,  y  =  0.0,           " 
13 +  25  P.O.  x=     0,  2^  =  0.0, 

The  location  of  this  curve  is  thiis  seen  to  be  a  very  simple  matter  ;  cal- 
culations for  the  circular  arcs  may  be  made  in  the  usual  manner,  and  the 
use  of  the  easement  curve  introduces  no  new  element  into  their  location, 
save  the  necessity  of  laying  them  tangent  to  lines  parallel  to  the  main 
tangents. 

The  tangent  distance  on  main  tangent  to  P.^.C  may  be  found  from. 

the  formula  Je  =  T  +  —  +  f,  in  which  Tia  the  tangent  distance  for  the 

curve  as  ordinarily  run,  -^  the  half-le      h  of  the  easement  curve,  and  t  a 

correction  due  to  shifting  the  point  of  intersection  (see  Fig.  I).  For  a 
simple  curve  with  the  same  shift  at  both  ends  t  =  s  tan  i  A*  For  a  simple 

curve  with  different  values  of  s  at  the  two  ends,  f ,-  =    .   ^ , s,    cot  A 

and  ?8  =  .  ^  —  Sg  cot  A«  For  a  compound  curve,  if  S3  be  shift  between 
circular  arcs,  s^  that  of  the  curve  of  larger,  and  s^  of  the  curve  of  smaller 

radius  from  the  tangent,  i^  =  — r  —  s^  cot^  and  #3  =  -: — ^ 

—  (Sg  +  S3  cos  As)  cot  /\,  +  s^sin  As- 

LOCATION  BY  DEFLECTION  ANGLES. 

K  the  values  of  x  in  Table  I  be  supposed  to  be  measured  on  chords  of 

the  easement  curve ;  and  if  a  be  the  angle  between  the  tangent  and  the 

V 
chord  to  any  point  distant  .r  from  the  P.E.C.,  then  sin  a  =  — ,  and  if  a 

table  of  the  values  of  a  for  each  curve  be  made,  the  curve  may  be  located 
on  the  ground  in  the  ordinary  manner  by  deflections  from  the  tangent. 


110  TRANSITION  OR  EASEMENT  CURVES. 

To  construct  this  table,  take  a  value  of  y  and  divide  it  by  the  correspond- 
ing value  of  X,  and  find  from  a  table  of  sines  the  angle  of  deflection,  then 

since  y  varies  as  the  cube  of  x,  —  varies  as  the  square  of  x,  and  as  for 

small  angles  the  sine  is  approximately  as  the  angle,  the  various  angles 
may  be  taken  as  varying  with  the  squares  of  their  distances.  In  this 
manner  any  column  of  Table  II.  may  be  constructed,  then  any  other 
column  may  be  found,  as  in  the  case  of  the  ordinates  in  Table  L,  by  con- 

sidering  that  for  constant  values  of  x,  —  varies  inversely  as  the  ratio 

between  the  length  of  curve  and  the  change  in  curvature. 

As  the  length  of  easement  curve  is  not  exactly  equal  to  the  sum  of  the 
lengths  measured  on  the  tangent  and  circular  arc,  a  correction  must  in 
some  cases  be  applied,  when  the  curve  is  to  be  located  by  this  method. 

This  correction  which  we  will  call  z,  is  to  be  substracted  from   -to  deter- 

mine  the  distance  to  be  measured  back  on  the  tangent  from  the  P.C.  to 
find  the  P.E^.C    Applying  this  correction  to  the  formula  for  tangent 

distance  we  have  3'e  =  T+t+  ^  —  z.    Values  of  z  are  given  in  Table 

m.,  found  by  calculating  the  co-ordinates  of  the  ends  of  the  easement 
curve  by  the  two  lines. 

In  order  to  lay  out  a  curve  by  this  method,  we  first  locate  the  P.E.C., 
and  placing  the  instrumenc  at  that  point,  turn  off  the  deflections  and  lay 
ont  the  curve  by  chords  of  any  desired  length,  interpolating  between  tiie 
numbers  in  the  table  for  the  angle  to  any  point  not  given.  To  pass  from 
a  circular  arc  to  the  tangent,  or  to  an  arc  of  greater  radius,  the  P.O.,  or 

point  of  osculation,  is  located  at  a  distance  -^  from  the  P.T.,  and  then  as 

the  deviation  of  the  easement  curve  from  the  circular  arc  is  the  same 
as  from  the  tangent,  the  deflection  to  any  point  of  the  easement  curve 
distant  x  from  the  P.O.  is  equal  to  the  deflection  for  the  circular  arc  for 
the  same  distance  minus  the  deflection  for  that  distance  as  given  in  Table 
II. ,  or  in  passing  from  a  curve  of  larger  to  one  of  smaller  radius,  the 
tabular  deflection  must  be  added  to  the  circular  deflection. 

As  an  illustration  of  this  method  suppose  that  it  be  required  to  locate 
the  curve  of  big.  1  by  means  of  deflection  angles.  It  will  not  be  neces- 
sary in  this  case  as  in  the  former  one  to  first  locate  the  circular  arcs,  but, 
having  found  the  P.E.C.,  set  the  instrument  over  that  point,  turn  off  the 


LOCATION  BY  ORDINATES.  HI 

deflections,  and  run  in  the  curve  in  the  ordinary  manner.  The  deflections 
for  the  first  easement  curve  may  be  taken  directly  from  Table  IL,  as  given 
below: 

Sta. 


9  +  05P.E.C 

X  = 

0 

9  +  50 

X  = 

45, 

a  =  0"05' 

10 

X   = 

95, 

a=      22 

10  +  50 

X  — 

145, 

a=:     52' 

11 

X   = 

195, 

a  =  1°35' 

11  +  50 

X   = 

245, 

a  =  2°30' 

12 

X   = 

295, 

a  =  3°37' 

12  +  25  P.O.      x^  320,    a  =  4°16' 

Having  located  the  P.O.  and  set  the  instrument  there,  we  turn  to  tan- 
gent by  deflecting  from  a  backsight  on  the  P.E.C.  an  angle  equal  to  twice 
the  last  forward  deflection,  2  (4°  16)  =  8°  32'.  In  other  words,  the  angle 
between  the  tangent  at  any  point  of  the  easement  curve,  and  the  chord 
connecting  that  point  with  the  P.^.C.  is  equal  to  twice  the  angle  between 
the  tangent  at  the  P.E.C.  and  the  same  chord. 

To  locate  the  easement  curve  connecting  the  circular  arcs,  having 
located  the  first  arc  DE,  (Fig.  1)  and  found  the  P.  O.  (^)  at  which  the 
second  easement  curve  begins,  suppose  this  point  to  come  at  station  17  + 
22.5;  the  deflections  for  this  easement  curve  from  the  circular  arc  ^Pwill 
then  be  the  same  as  those  of  the  first  curve  from  the  tangent  AB,  or  the 
deflections  from  the  curve  EH  from  the  tangent  at  E,  will  equal  the  de- 
flections for  the  arc  EF,  minus  the  deflections  from  Table  IL  for  the  ease- 
ment curve,  and  may  be  tabulated  as  follows: 

Sta.  17+22.5  P.O.  «=    0 

17+50  x=  27.5,  deflection  =1°06  — 0°02=1^04' 

18  x=  77.5,  "  =3°06'— 0n5'=2°51' 

18+42.5  P.O.  a;=  120.0,  "  =4^48'-0°36=4n2' 

To  find  the  tangent  at  18+42.5  {P.O.),  turn  from  the  last  chord  an  angle 
—  deflection  for  120'  of  8"^  curve,  (4°48')  minus  twice  (deflection  for  120'  of 
easement  curve),  (2x36'=72')=:3'36',  or  this  angle  may  be  found  thus;  de- 
flection for  120'  of  5°  curve,  (3°00')  plus  deflection  for  120'  of  easement 
curve,  (36)  =  3=36'. 

In  the  same  manner  having  run  the  5°  circular  arc,  we  can  tabulate  the 


112  TRANSITION  OR  EASEMENT  CURVES. 

deflections  necessary  to  connect  it  with  the  tangent,  supposing  the  P.O- 
to  be  at  sta.  33  +  13.5. 

23+13.5  P.O.  xz=      0 

23+50  x=  36.5,  deflection  =0°55'— 0°03'=0°58* 

24  x=  86.5,         "  =2°10'-0°]9'=1°51' 
24+50                a;=rl36.5,         "  =3°25— 0°47'=2°38' 

25  a;=176.5,         "  =4°40'— 1°37'=3°13' 
25+13.5  P.7i7.r.a;=200,           "  =5°00'— 1°40'=3°20' 

Then  turn  to  the  tangent  at  M,  by  deflecting  from  the  last  chord,  one- 
half  the  last  deflection,  i  (3°20')  =  r40'  =  the  deflection  for  200  ft.  of  the 
easement  carve. 

The  deflection  from  the  P.  E.  C.  to  any  point  x  of  the  easement  curve 
is  equal  to  one-third  of  the  deflection  for  the  same  length  of  the  circular 
arc,  whose  radius  is  equal  to  the  radius  of  curvature  of  the  easement 
curve  at  the  point  x;  also,  the  difference  between  the  circular  deflections 
at  any  two  points  of  an  easement  curve,  for  a  length  equal  to  the  dis- 
tance between  the  points,  is  equal  to  three  times  the  easement  deflection 
for  the  same  length. 

In  case  it  be  necessary  to  set  the  instrument  at  any  intermediate 
point  upon  the  curve,  this  enables  us  to  readily  find  the  deflections  for 
the  circular  arc  at  that  point.  Thus,  if  we  desire  to  set  the  instrument  at 
station  24  in  the  above  example,  we  first  turn  to  tangent  at  24  by  deflect- 
ing 2°  10'  —  2  X  19'  =  1°  32'  from  the  last  chord. 

Then  the  deflection  for   86,5  ft.  of    the  circular   arc,  whose  radius 

equals  the  radius  of  curvature  of  the  easement  curve   at  station   24 

50 
is  2°  10'  —  3  X  19'  =  1°  13',  and  the  deflection  for  50  ft.  is  „„  ^  (1°  13') 

=  42'   or,  as  the  point  24  is  113.5  ft.    on  the    easement    curve  from 
the  tangent,  easement  deflection  for  113.5  ft.  is  32'   (Table  II.),  and 
50 

^2'x^x  n3:5  =  ^'- 

Then  the  deflections  from  tangent  at  24  for  the  remainder  of  the  curve 
would  be 

Sta.  24  a;  =     0, 

24  +  50  x=    50,    deflection  =     42'  —  06'  =  0°86' 

25  x  =  100,  "         =  1°24'  —  25'  =  0°59' 
25  +  13,5  P.E.T.   X  =  113,5,         "  =  1°36'  —  32'  =  1°04' 

As  will  be  seen  by  an  inspection  of  the  tables,  the  few    curves   tabulated 


SPECIAL  CASES.  113 

afford  considerable  range  for  choice  of  a  curve  for  any  particular  case, 
and  will  give  considerable  elasticity  to  the  work  of  placing  the  location 
by  allowing  the  use  of  various  shifts.  Tables  affording  a  much  larger 
choice  may  readily  be  constructed,  and  will  occupy  but  a  small  space 
while  answering  all  the  requirements  of  any  practical  case. 

Note. — It  is  to  be  noticed  that  the  two  methods  of  location  above  out- 
lined do  not  give  exactly  the  same  curve,  and  hence  are  not  interchange- 
able except  within  the  limits  where  z  is  zero.  Outside  these  limits  the 
length  of  the  curve  located  by  ordinates  will  exceed  the  distance  meas- 
ured upon  the  tangent  and  circular  arc  by  a  quantity  approximately 
equal  to  z.  The  values  of  z  will  vary  somewhat  with  the  use  of  different 
chord  lengths  in  location.  In  a  case  where  extreme  accuracy  is  required 
a  small  correction  should  also  be  applied  to  the  shift ;  within  the  limits 
covered  by  these  tables,  however,  this  correction  would  be  inappreciable 
for  any  ordinary  work.  Evidently  the  methods  used  for  the  deflections  is 
only  applicable  to  small  angles,  as  it  is  an  approximation  and  not  theo- 
retically exact,  and  if  continued  to  larger  angles  the  deflections  will  no 
longer  equal  one-third  of  the  central  angle,  and  corrections  must  be  ap- 
plied. Most  cases  in  practice  will,  however,  probably  be  well  within  the 
limits  of  the  tables  given. 

SPECIAL  CASES. 

It  is  frequently  necessary  to  replace  circular  curves  already  in  use  by 

others  connecting  the  same  tangents  and  passing  through  certain  points 

whose  positions  are  known.    All  such  cases  may  be  met  by  the  foregoing 

methods,  the  solution  in  each  case  varying  with  the  data  given. 

As  an  illustration  take  one  of  the  most  common  cases.    Let  ABC  (Fig. 

2)  be  an  8°  circular  curve  700  ft. 
long,  which  is  to  be  replaced  by  a 
new  circular  arc,  passing  through 
the  same  vertex  {B)  and  joined  to 
the   same   tangents    by    easement 
curves    in    which    the    curvature 
change  1°  for  each  30  ft.  of  dis- 
tance.   The  shift  for  the  8°  curve 
from  Table  I.  is  3.3  ft.,  but  the  new  arc  will  be  of  less  radius  than  the  8° 
and  the  shift  greater;  assume  it  at  4.0  ft.,  then  the  external  distance 
{DB)  of  the  8°  curve  =  R.  ex.  sec  \/\,  =  716.779  X  .13257  =  95,02/f. 
DE  =  OH  sec  iA  =  «  ««c  iA- 


114 


TRANSITION  OR  EASEMENT  CURVES. 


BE  (the  external  distance  for  the  new  arc)  =  BD  —  DE  =  95.02 
—  4    X    1.13357   =   90.49  ft.,    and    the    radius    of   the    new    arc   = 

=   ,  '  ..,  =  683.6  ft.  or  the  rate  of  curvattire  of  the  new 

ex.   see  i   a        .13357  •' 

arc  is  8°  84' . 

The  length  of  easement  curve  to  vary  1°  in  30  ft.  is  then  253  ft.,  the 
half-length  136/<.,  and  (from  the  table)  the  half-shift  is  1.95  or  s  =  3.9^ 
which  shows  that  our  assumption  of  4.0  ft.  for  the  shift  is  sufficiently 
accurate  ;  in  case  it  were  not,  it  would  be  necessary  to  try  a  new  one. 

Now  from  B,  the  8^  24'  curve  may  be  located  ending  at  i^and  G,  or  the 
tangent  distance  may  be  computed  from  the  formula,  and  the  P.E.C. 
located  after  which  the  curve  may  be  placed  by  tlie  use  of  the  tables  as  in 
the  former  cases. 

If  it  be  desired  to  shift  the  vertex  of  the  new  curve  any  distance  either 
outward  or  inward  from  the  original  curve,  it  will  simply  be  necessary  to 
subtract  such  distance  from  or  add  it  to  the  external  distance  in  finding 
the  radius  of  the  new  curve. 

TABLE  I.— ORDINATES  FOB  LOCATIXG  THE  CUBIC  PARABOLA. 


Curvature  changes  1®  for  every 

Values 

of  X. 

20  feet. 
0.00  feet. 

25  feet. 

30  feet. 

35  feet. 

40  feet.       45  feet. 

50  feet. 

10  feet. 

0.00  feet. 

0.00  feet. 

0.00  feet. 

0.00  feet. 

0.00  feet. 

0.00  feet. 

20    •' 

0.01    *' 

O.Ol    " 

0.01    " 

0.01    " 

0.01    " 

0.00    " 

0.00    " 

30    " 

0.04    " 

0.03    " 

0.03    " 

0.02    " 

0.02    " 

0.02    " 

0.02    " 

40    " 

0.09    " 

0.07    " 

0.06    " 

0.05    " 

0.05    " 

0.04    " 

0.01    " 

50    " 

0.18    " 

0.14    " 

0.12    " 

0.10    " 

0.09    " 

0  08    •' 

0.07    •' 

60    " 

0.31    " 

0.25    " 

0.21    •' 

0.18    " 

0  15    " 

0.14    " 

0.13    " 

VO    " 

0.-50    " 

0.40    " 

0.32    " 

0.28    " 

0.25    " 

0.22    " 

0.20    " 

80    " 

0.74    " 

0.60    " 

0.49    " 

0.42    " 

0.37    " 

0.33    •' 

0.30    '■ 

90    •• 

1.06    " 

0.85    " 

C.70    " 

0.60    " 

0.53    " 

0.47    •' 

0.42    " 

100    " 

1.45    " 

1.16    " 

0.97    " 

0.83    " 

0.73    " 

0.65    " 

0.58    '• 

no  " 

1.93    " 

1.55    " 

1.29    " 

1.10    " 

0.96    " 

0.86    " 

0.77    " 

120    " 

2.51    " 

2.00    " 

1.67    " 

1.43    " 

1.25    " 

1.12    " 

1.00    " 

130    " 

3.19    " 

2.50    " 

2.13    " 

1.83    " 

1.60    " 

1.42    " 

1.28    " 

140    " 

3.98    " 

3.20    " 

2.66    " 

2.29    " 

2.00    " 

1.77    " 

1.60    " 

150    •' 

4.90    " 

3.92    " 

3.27    " 

2.80    " 

2.45    " 

2.18    " 

1.96    " 

160    " 

3.39    '• 

2.97    " 

2.64    " 

2.38    •• 

170    " 

4.08    " 

3.57    " 

3.17    " 

2.85    " 

180    " 

4.81    '• 

4.24    " 

3.76    " 

3.38    '• 

190    " 

5.69    " 

4.98    " 

4.43    " 

3.98    " 

200    " 

6.64    " 

5.81    " 

5.16    " 

4.64    " 

210    " 

5.98    '• 

5.38    •' 

220    " 

6.87    •' 

6.19    " 

230    " 

7.85    " 

7.07    " 

240    " 

8.92    " 

8.03    " 

260    " 

10.09    '* 

9.08    " 

SPECIAL  CASES. 

TABLE  II.— DEFLECTION  FOB    LOCATING    THE    CUBIC   PARABOLA. 


115 


Values 

Curvature  chansres  1**  for  each 

of  x. 

20  feet. 

25  feet. 

30  feet. 

35  feet. 

40  feet. 

45  feet 

50  feet. 

10  feet 

0"  00' 

O"  00' 

0°  Oft' 

0"  00' 

0«  00' 

0"  00 

0"  00' 

20  " 

02 

02 

01 

01 

01 

01 

01 

30  " 

05 

0( 

03 

03 

02 

02 

02 

40  " 

08 

00 

05 

04 

04 

03 

03 

50  " 

13 

10 

08 

07 

06 

06 

05 

60  " 

18 

15 

12 

10 

09 

08 

07 

70  " 

25 

20 

16 

14 

12 

11 

10 

80  " 

32 

26 

21 

19 

16 

14 

13 

90  " 

40 

32 

27 

23 

20 

18 

16 

100  " 

50 

40 

33 

29 

25 

22 

20 

110  " 

1 

48 

40 

34 

30 

27 

21 

120  " 

00 

58 

48 

41 

.36 

32 

29 

130  " 

12 

1  08 

56 

49 

42 

38 

31 

140  " 

25 

18 

1  05 

56 

49 

43 

39 

150  " 

38 
52 

30 

15 

1  04 

56 

50 

15 

160  " 

2  08 

42 

25 

13 

1  04 

57 

51 

170  " 

25 

56 

36 

23 

12 

1  04 

58 

ISO  " 

42 

2  10 

48 

33 

21 

12 

1  05 

190  " 

3  00 

24 

2  00 

ii 

30 

20 

12 

200  " 

'JO 

10 

13 

54 

40 

29 

20 

210  " 

40 

56 

27 

2  06 

50 

38 

28 

220  " 

4  02 

3  14 

41 

17 

2  01 

47 

37 

230  " 

25 

32 

56 

31 

12 

58 

46 

240  " 

48 

50 

3  12 

45 

24 

2  08 

55 

250  " 

5  12 

4  10 
30 

28 

59 

36 

19 

2  05 

260  " 

38 

52 

45 

3  13 

49 

30 

15 

270  " 

6  05 

4  03 

29 

3  02 

42 

28 

280  " 

32 

5  14 

21 

41 

16 

64 

37 

290  •' 

7  00 

36 

40 

4  00 

30 

3  07 

48 

300  " 

7  30 

6  00 

5  00 

17 

45 

20 

3  00 

310  " 

4  34 

4  00 

3  33 

3  12 

321  " 

43 

16 

48 

25 

330  " 

5  11 

32 

4  02 

38 

340  " 

30 

49 

17 

51 

350  " 

50 

5  06 

32 

4  05 

,360  " 

24 

48 

19 

370  " 

42 

5  04 

31 

380  " 

6  01 

21 

49 

390  " 

20 

38 

5  04 

400  " 

40 

65 

20 

410  •' 

6  la 

3ii 

420.  " 

32 

53 

430  •• 

41 

6  10 

440  " 

7  10 

27 

450  " 

30 

45 

460  " 

7  03 

470  " 

22 

480  " 

4(1 

490  " 

8  00 

500  " 

■10 

116 


TRANSITION  OR  EASEMENT  CURVES. 


TABLE  III.— VALUES  OF  Z. 

Minus  Correction  for  Tangent  Listance  of  Easement  Curve  Located  by  Deflection 

Angles 


Curvature  changes  1° 

for  eeich 

Degree 

of  Curve. 

20  feet. 

25  feet. 

30  feet. 

35  feet. 

40  feet. 

45  feet. 

50  feet. 

6deg. 

0.1  feet. 

0.1  feet. 

0  1  feet. 

7    " 

0.1  feet. 

0.1  feet. 

0.2     " 

0.2     •' 

0  3" 

8    " 

0.1  feet. 

0.2     " 

0.3     " 

0.4     " 

0.5     " 

0.6     ■' 

9    •• 

0.1  feet. 

0.2     " 

0.4     " 

0.5     •• 

0.7     " 

0,8     " 

l.I     " 

10    " 

0.2     " 

0,3     " 

0.6     ' 

0.8     " 

1.0     " 

1.3     " 

1.7     " 

H    " 

0.3     " 

0.5     " 

12    " 

0.4     " 

0.7     " 

13    " 

0.6     •• 

14    " 

0.8     " 

15    " 

1.1     " 

ELEVATION  OF  OUTER  RAIL  ON  CURVES. 
The  elevation  of  the  outer  rail  is  constant  throughout  the  curve.    Its 
theoretical  amount  (see  •'  Henck's  Pocket  Book  ")  is     f      -,  in  which  g  is 
the  gauge,  v  is  the  velocity  of  the  train,  and  R  is  the  radius  of  the  curve. 


If  g  if,  4.7  and  v  is  40.44  or  27.57  miles  per  hour,  this  reduces  to 


or,  if  the  elevation  is  in  inches  and  the  radius  in  feet,  to 


2,864 
R 


238.7 
R    ' 

But  this 


numerator  is  the  radius  of  a  two-degree  curve,  from  which  the  rule  is 
deduced  which  is  adopted  on  many  railroads:  "  Elevate  the  outer  rail 
one-half  an  inch  for  each  degree  of  curve."  Thus,  for  a  two-degree  curve 
elevate  one  inch,  and  for  a  six-degree  curve,  elevate  three  inches. 

If  a  circular  curve  starts  directly  from  a  tangent,  theory  requires  an 
abrupt  elevation  at  the  point  of  curvature.  As  this,  however,  is  impracti- 
cable, the  elevation  is  usually  run  out  on  the  first  rail  (or  the  first  two) 
from  the  point  of  curvature,  the  rail  being  at  the  height  of  the  elevated 
rail  at  one  end,  and  at  the  height  of  the  opposite  rail  at  the  other  end. 
To  avoid  the  theoretical  difficulty  of  the  sudden  elevation  of  the  outer  rail, 
parabolic  curves  have  been  proposed,  the  radius  of  curvature  at  the  be- 
ginning of  the  curve  being  so  long  as  to  be  practically  infinite,  which 
would  require  no  elevation;  and  as  the  radius  became  gradually  shorter 
to  the  middle  of  the  curve,  the  outer  rail  could  be  proportionately  elevated. 
The  additional  labor  involved  in  laying  out  the  curves,  and  giving  this 


ELEVATION  OF  OUTER  RAIL  ON  CURVES.  117 

variable  elevation,  has  prevented  the  general  introduction  of  parabolic 
curves  in  this  country.  However,  the  end  of  maJsing  the  elevation  pro- 
portional to  the  curvature  gradually  is  accomplished  by  putting  in,  at 
each  end  of  the  curve,  what  is  called  a  "  curve  of  adjustment"  when  the 
rails  are  being  laid,  which  is  an  "  elastic  curve,"  and  is  laid  out  by  offsets 
from  the  centre-line  stakes,  the  latter  being  set  on  tangents  and  circular 
curves.  The  method  of  laying  out  the  elastic  curve  is  given  in  the  pre- 
ceding pages.  It  seems  to  be  the  English  practice  to  obtain  the  proper 
elevation  of  the  outer  rail  by  raising  the  outer  rail  one-half  of  the  proper 
amount  and  depressing  the  inner  rail  by  the  same  amount.  In  the  United 
States,  however,  it  is  generally  all  put  in  the  outer  rail,  the  inner  rail 
carrying  the  grade  of  the  road. 


CHAPTER  VI. 


Earthwork  and  Masonry. 

ESTIMATING  OVERHAUL  IN  EARTHWORK  BY  I^IEANS  OF  THE 
PROFILE  OF  QUANTITIES. 


By  S,  B.  Fisher,  Chief  Engineer  of  the  Minneapolis,  St.  Paul  & 
Sault  Ste.  Marie  Ry.,  Minn. 


No  facile,  practical  and  accurate  method  of  calculating  the  overhaul  of 
earthwork  is  as  yet  in  common  use.  The  problem  itself,  consisting  of 
finding  the  relations  between  the  centers  of  gravity  of  known  volumes  in 
known  positions  may  be,  from  the  mathematician's  point  of  view,  a  com- 
paratively simple  one;  but  such  a  lack  of  readiness  to  solve  it  has  the 
engineer  shown  that  many  a  contract  has  been  executed  with  the  privi- 
lege of  wasting  and  borrowing  at  the  end  of  the  haul.  This  practice 
results  at  times  in  waste  of  energy  by  the  contractor,  and  still  oftener  in 
the  wasfe  of  money  to  the  other  party  to  the  contract.  By  the  system  of 
wasting  and  borrowing,  material  is  paid  for  at  the  full  price  of  excavation 
beyond  the  haul,  but,  with  the  judicious  use  of  overhaul,  in  many  cases 
the  material  may  be  hauled  half  a  mUe  before  its  price  is  doubled. 
When,  from  the  increase  of  the  trafiic  of  a  railroad,  for  example,  it  be- 
comes necessary  to  grade  for  a  second  track,  and  in  so  doing  to  remove 
material  wasted  on  the  margin  of  a  cut  into  an  adjoining  borrow  pit  along 
the  neighboring  fill,  where  it  ought  to  have  been  deposited  in  the  first 
place,  it  neither  increases  the  respect  of  the  later  engineers  for  their  pre- 
decessors, nor  is  it  a  credit  to  the  profession. 

Overhaul  as  commonly  worked  out  is  done  in  an  approximate  manner 
with  the  ordinary  profile  and  the  volumes  in  excavation  and  embank- 
ment.   It  takes  longer  to  work  it  out  with  the  "  Profile  of  Quantities,"  of 


COMPILATION  OP  THE  DATA. 


119 


which  a  short  example  is  engraved,  but  it  is  done  completely  and  accu- 
rately. 

The  method  of  the  profile  of  quantities  was  originated  by  Briickner,  a 
Bavarian  engineer.  It  was  presented  by  Cuhlman  in  bis  "  Graphical  Stat- 
ics "  in  1868,  and  translated  from  that  by  F.  Reineker,  then  (1871-8) 
Principal  Assistant  Engineer  of  the  Pennsylvania  Co  ,  at  Pittsburg,  Pa  , 
for  the  use  of  his  department.  This  translation  was  procured  there  by 
the  writer,  and  the  method  adapted  to  American  practice  in  a  great 
variety  of  railway  work,  and  is  here  given  with  an  example  of  work  as 
actually  executed. 

The  subject  is  presented,  for  convenience  and  clearness,  in  three 
steps — 

1st.  The  Compilation  of  the  Data.  2d.  The  Plotting  of  tlie  Profile. 
3d.  The  Taking  Off  of  the  Results. 

I.      COMPILATION  OF  THE  DATA. 

The  paper  containing  the  data  is  ruled  in  five  vertical  columns,  as  in  the 
following  sample  table : 

Sample  Table  of  Computations  for  Constructing  "  Profile  of  Quantities  " 
O.  &  S.  W.  R.  R.  data  for  Profile  of  Quantities,  Section  5,  Oct.  1,  1889. 


Sta. 

Incre- 
ments. 

Ordinates. 

Sta. 

Incre- 
ments 

Ordinates. 

Sta. 

Incre- 
ments. 

Ordinates . 

+ 

- 

+ 

- 

+ 

- 

+ 

- 

+ 

- 

+ 

- 

213+34 
214 

5 

6 

7 

8 

9 
220 

1 

2 

3 

i 

5 

6 

7 

8 

9 
230 

■376 
843 
779 
724 
902 
570 
391 
457 
535 
678 
723 
344 
193 
156 
244 
221 
356 

""376 
1,213 
1,991 
2,715 
3,617 
4.187 
4,578 
5,0.35 
5.570 
6,248 
6.973 
7,317 
7,510 
7,666 
7.910 

8.ni 

8,487 

1 
2 
3 
4 
5 
6 
7 
8 
9 
240 
1 
2 
3 
4 
5 
6 
7 
8 

iei 

328 
484 
493 
411 
367 
281 
221 
200 
180 
185 
156 
102 
59 

317 
83 

14 
70 

-  .. 

8,804 
8,887 
8,726 
8,398 
7.934 
7,441 
7,030 
6,663 
6,379 
6,155 
5.955 
5,770 
5,585 
5,429 
5,327 
5,258 
5,272 
5,342 

9 
250 
1 
2 
3 
4 
5 
6 
7 
8 
9 
0 
1 
2 
3 
4 
5 
6 

"55 
156 
102 
146 
2«16 
237 
250 
274 
47 

83 
78 
65 
70 
124 
181 
189 
!:5 

■"6 

5,425 
5,503 
5,568 
5,638 
6,762 
5,943 
6,132 
6.217 
6,0c2 
5896 
5,794 
5,658 
5,452 
5,215 
4,965 
4,691 
4,641 
4,650 

The  first  column  contains  the  station  numbers.  In  practice  the  ele- 
mental volume  is  the  total  excavation  or  embankment  in  a  full  station, 
whether  the  station  distance  is  100  ft.,  66  ft.,  or  a  number  of  metres. 


120 


EARTH  WORK  AND  MASONRY. 


«pj»A   aigrvQ 


'W^/t   ■'ii'io 


Plufises  are  not  used,  excepting  at 
an  occasional  beginning  or  end  of 
a  subsection,  although  the  system 
is  flexible  enough  to  apply  to  any 
regu  lar  or  irregular  subdivision  of 
these  elemental  volumes. 

In  columns  2  and  3  are  now  en- 
tered the  total  increments  or  vol- 
umes of  earthwork  in  excavation 
or  embankment  in  successive  sta- 
tions. When  excavation  and  em- 
bankment both  occur  within  the 
limit  of  the  same  station  the  net 
amount  only  need  be  entered.  If 
there  is  a  special  price  for  casting 
within  the  station  another  column 
may  be  introduced  for  it.  Exca- 
vation is  considered  plus  and  em- 
^  bankment  minus.  The  latter  may 
I  be  entered  in  red  ink. 
^ J  Columns  4  and  5  are  now  filled 
up  by  algebraic  addition  of  col- 
umns 2  and  3.  The  ordinate  at  any 
point  of  the  "Profile  of  Quantities" 
is  equal  to  the  algebraic  sum  of  the 
volumes  as  far  as  to  that  point,  and 
should  be  verified  by  use  of  this 
principle,  at  convenient  points,  as 
the  summation  proceeds. 

II.     THE  PLOTTING  OF  THE  PROFILE. 

The  horizontal  part  of  the  plot- 
ting is  the  same  as  used  in  the  or- 
dinary profile,  and  it  may  be  made 
on  the  same  sheet  of  paper;  but  for 
the  vertical  part,  instead  of  eleva- 
tions being  referred  to  a  datum 
plane,  at  or  below  the  lower  edge 
of  the  profile  paper,  we  have  an 
initial  line  or  axis  of  abscissas,  lo- 


TAKING  OFF  THE  RESULTS.  181 

cated  some  where  on  the  profile,  from  which  the  ordinates  are  measured 
above  for  plus  and  below  for  minus.  Connecting  the  ends  of  these  ordinates, 
we  have  a  broken  line,  which  in  mathematical  language  may  be  called  a 
curve,  resembling  somewhat  an  ordinary  profile,  but  wholly  different 
therefrom,  composed  of  the  elements  between  the  successive  stations. 

If  the  increment,  by  the  use  of  which  any  ordinate  is  formed  from  the 
previous  one,  is  positive,  this  element  of  the  curve  will  incline  upward, 
will  indicate  excavation,  and  be  shown  by  a  dotted  or  blue  line.  If  the 
increment  is  negative  tbe  element  of  the  curve  will  incline  downward, 
wall  indicate  embankment  and  be  shown  in  red  or  by  a  solid  line.  So 
that  excavation  on  the  profile  of  quantities  is  always  sbownby  an  ascend- 
ing dotted  or  blue  line,  and  embankment  by  a  descending  solid  or  red 
line. 

We  now  consider  the  balancing  line.  Some  points  of  this  line  are 
always  fixed  by  the  patent  conditions  of  the  work,  and  occasionally  all 
points  are  so  fixed,  but  very  often  some  points  on  it  are  indeterminate  at 
first,  so  that  each  section  is  very  likely  to  be  a  little  problem  by  itself. 
The  functions  of  the  balancing  line  will  most  clearly  be  seen  by  referring 
to  the  engraved  sample  profile.  We  have  here  the  first  point  of  it,  A,  the 
beginning  of  the  section;  B,  the  end  of  Ole  Olson's  job;  C,  the  end  of  John 
Johnson's  job;  D,  the  end  of  Teapot  Kofeeson's  job;  E,  at  station  240, 
the  dividing  point  "between  backward  and  forward  hauls  in  the  cut;  F, 
station  252+30;  J,  junction  point  of  forward  and  backward  hauls  in  the 
fill;  G,  the  point  where  waste  commences  in  the  second  cut,  and  H,  the 
end  of  the  section. 

III.      THE  TAKING  OFF  THE  RESULTS. 

From  Ato  D  there  is  no  over  haul,  but  the  natiire  of  the  material  and 
any  other  items  can  be  conveniently  recorded  there.  The  fill  between  D 
and  K  is  made  from  tbe  cut  between  K  and  E.  We  first  fix  the  position 
of  the  limit  of  haul,  which  here  comes  between  stations  226  and  236,  and 
then  draw  the  intervening  lines  of  over  haul  to  each  point  of  flexure  of 
blue  and  red  lines.  We  now  read  the  elements  of  the  cut  between  these 
lines  of  haul,  from  the  profile  m,  or  if  we  desire  great  accuracy,  from  the 
data  prepared  for  plotting  the  profile  n,  and  tabulate  them.  Each  of  these 
elements  multiplied  by  its  respective  distance  overhauled  will  give  equiva- 
lent quantities  overhauled  to  one  station;  as  for  example, 
1,680  +  1,570 

224  cy  X 1,000  =  224  X  6.25  =  1,390.    The  sum  of  these 

2 
partial  products  wUl  give  the  total  overhaul  for  the  cut.    The  tabulation 


122  EARTH  WORK  AND  MASONRY. 

should  always  be  verified,  by  seeing  that  the  sum  of  the  elements  of  the 
blue  or  red  curve,  as  the  case  is,  is  equal  to  the  difference  between  the  ex- 
treme ordinates. 

If  ^  X  is  rock  or  D  K  is  a  sink  hole,  the  line  E  D  wiU  be  inclined,  and 
should  be  prolonged  to  an  intersection  with  the  horizontal  through  K. 
This  intersection  then  becomes  a  pole,  through  which  the  lines  of  haul 
are  drawn.  The  method  is  so  flexible  it  can  be  applied  to  anything 
which  can  be  executed  in  earthwork,  and  in  addition  gives  a  record  of 
what  has  been  done.  It  is  also  used  to  make  the  preliminary  distribution 
of  material  before  the  w^oik  is  begun. 

NpTE.— For  the  further  discussion  of  this  subject  see  Engineering  News  of  April 
i,  1883,  and  March  14,  1891. 

EXPANSION  OF  ROCK  IN  EMBANKMENT. 
The  following  are  data  of  an  accurate  test  made  at  Boulder,  Colo.,  in 
1882  on  expansion  of  solid  rock  from  cut  to  embankment.  The  point 
chosen  offered  these  advantages :  material  all  solid  rock,  free  from  an 
overlying  earth  ;  surface  uniform,  admitting  of  accui-ate  measurement  ; 
no  possible  settling  of  the  embankment,  as  it  was  directly  on  granite  cow- 
pastures  ;  volume  of  the  work  9,000  cubic  yards  in  400  ft.  lengths,  re- 
ducing wastage  from  blasts  to  a  minimum,  and  lastly,  its  location  being 
such  that  it  was  seen  several  times  every  day.  Results  as  follows  :  Rock 
in  excavation  and  borrow  pit  measured  in  place  3.596  yds.;  the  same  ma- 
terial, measured  in  embankment,  yielded  5,387  yds.,  or  an  expansion  ratio 
of  1  : 1.512. 

NOTES  ON  EARTHWORK.* 

In  making  the  final  estimates  of  the  St.  Gothard  Railroad,  the  quanti- 
ties in  cut  were  increased  by  '3%  in  earth  and  8%  in  rock,  to  equalize  the 
amounts  needed  for  embankments. 

In  the  levee  work,  under  the  direction  of  the  writer,  the  following  pro- 
portions were  observed  : 

9,398  cubic  yards  in  cut  gave  9,470  in  fill  (ground  :  heavy  adobe,  meas- 
ured three  weeks  after  finished). 

10,000  cubic  yards  in  cut  gave  10,290  in  fill  (ground:  adobe  in  sandy  loam) 

29,000  cubic  yards  in  cut  gave  30,330  in  fill  (ground  :  the  same  as  last). 

53,350  cubic  yards  in  cut  gave  58,350  in  fill  (ground  :  sandy  loam  with 
small  amounts  of  adobe  and  hard  pan;  this  is  the  largest  increase  found). 

*  Read  by  the  late  Geo.  J.  Specht  before  the  Technical  Society  of  the  Pacific  Coast, 
May  1, 1885. 


NOTES  ON  EARTHWORK.  123 

203,634  cubic  yards  in  cut  gave  208,915  in  fill  (this  represents  the  work 
of  three  months). 

The  concJusion  is,  that  no  general  coefficient  can  be  established  to  ex- 
X)ress  the  proportion  of  earth  or  rock  in  place  to  earth  or  rock  in  fill.  It 
is  different  with  different  kinds  of  material  and  with  the  different  meth- 
ods of  building  the  embankments. 

A.  Von  Kaven,  President  of  the  Royal  Polytechnic  Institute  in  Aix-Ia- 
Chapelle,  says  in  his  book  on  "  road  building"  : 

"  The  volume  of  an  embankment  and  its  height  are  different  at  differ- 
ent times.  European  experience  is  road  building  is  that,  after  the  fill  is 
finished,  the  earth  used  therein  occupies  a  larger  space  than  in  the 
ground  : 

In  clay  and  loam 1-48  more. 

In  soft  sandstone 1-32     " 

In  hard  clay 1-20     " 

In  rock 1-13  to  1-10     " 

"  During  the  construction  of  the  Rhine-Nahe  Railroad  it  was  observed 
that  the  increase  in  bulk  from  cut  to  fill  was  in  the  beginning  25  per  cent, 
in  rock,  but  when  from  one-quarter  to  one-third  of  the  total  bulk  of  the 
embankment  was  built  of  clay^  put  in  simultaneously  with  the  rock,  the 
final  increase  in  embankment,  after  the  same  was  finished,  was  only  9  per 
cent.  There  are  certain  kinds  of  earth  and  certain  conditions  during  the 
time  of  building,  when  the  embankment,  occupies  less  space  than  the 
earth  measured  in  place.  For  instance,  if  the  earth  is  wet,  or  if  it  is 
tamped,  etc.  The  French  engineer,  Graeff,  says  that  1  cubic  metre  of 
rock  measured  1.5  to  1.6  whenever  in  fill,  but  as  considerable  earth  was 
used  with  it  to  fill  the  intermediate  spaces,  1  cubic  metre  cut  made  1  cubic 
metre  fill  in  a  general  average. 

"  In  building  the  Marne-Rhine  canal  the  loose  earth  was  carefully 
tamped  and  1  cubic  metre  embankment  required  1.10  to  1.25  cubic  metre 
in  cut.  He  advises,  therefore,  not  to  count  on  any  difference,  but  to  ac- 
cept cut  and  fill  alike,  and  allow  only  in  very  light  sand  a  decrease  of  one- 
tenth  in  fill. 

'"According  to  a  series  of  observations — 
"  100  cubic  feet  of  loose  sand  make  115-120  cubic  feet  in  fill. 
"  100  cubic  feet  of  clay  and  coarse  sand  make  123  cubic  feet  in  fill. 
"  100  cubic  feet  of  hard  clay,  lias,  make  124  cubic  feet  in  fill. 
"  100  cubic  feet  of  clay  mixed  with  cobble-stones  make   126  cubic  feet 
infiU. 


124  EARTHWORK  AND  MASONRY. 

"  100  cubic  feet  of  decomposed  rock,  solid  gravel  banks,  make  128  cabic 
feet  in  fill. 

"  100  cubic  feet  of  rock  (can  be  picked)  make  130  cubic  feet  in  fill. 

"  100  cubic  feet  of  rock,  requiring  blasting,  make  134-150  cubic  feet  in 
fill." 

llenz,  the  author  of  a  Manual  on  Earthwork,  states  as  the  result  of  a 
large  number  of  observations  of  actual  work,  that  the  permanent  increase 
in  volume  from  cut  to  fill  is— 

In  sandy  soil 1-1.5  per  cent. 

In  clay  and  light  soil 3  " 

In  marl 4-5  " 

In  hard  clay 6-7  " 

In  rocK 8-12         " 

J.  C.  Trautwine,  in  his  "  Pocket-Book,"  says:  ''Although  earth  when 
first  dug  and  loosely  thrown  out,  swells  about  ^  part,  so  that  a  cubic  yard 
in  place  averages  about  1|  or  1.2  cubic  yards  when  dug  ;  or  1  cubic  yard 
when  dug  is  equal  to  f  or  0.8333  of  a  cubic  yard  in  place  ;  yet  when  made 
into  embankment  it  gradually  subsides,  settles  or  shrinks  into  a  less  bulk 
than  it  occupied  before  being  dug. " 


EARTHWORK    COMPUTATION. 

A.    M.   WELLINGTON. 

1.  Compute  solidities  by  averaging  end  areas  and  use  the  results  for  all 
prpliminary  purposes,  monthly  estimates,  etc. 

2.  At  any  time  before  the  final  estimate,  substract  the  center  heights 
only  from  each  other  of  those  solids  only  which  differ  three  feet  or  more 
in  center  height. 

3.  Determine  a  correction  to  be  applied  to  each  of  such  solids  from  a 
tabulation  of  the  following  formula  : 

Correction  in  cu.  yds.  =  g — ^  X   07" 

in  which  c  and  c  e'  =  center  heights,  r  =  ratio  of  slope  and  I  =  length  of 
solid  =  100  feet  for  purposes  of  the  table. 

(Such  a  table  can  be  made  in  a  few  minutes,  as  it  is  required  only  from 
3  to  10  or  12  feet  ranging  by  tenths.) 

4.  Determine  the  sum  of  these  corrections  for  any  given  section  and 
deduct  them  in  gross  from  the  end  area  solidity,  for  final  estimate  pur- 
poses. 


LEVEE  CONSTRUCTION.  125 

LEVEE  CONSTRUCTION. 

The  following  methods  of  construction  are  those  adopted  by  the  Board 
of  Mississippi  Levee  Commissioners  and  their  Chief  Engineer: 

The  ground  to  be  occupied  by  the  levee  must  first  be  cleared  of  trees, 
stumps,  logs,  trash,  weeds  and  all  perishable  matter ;  the  trees  and 
stumps  being  cut  level  with  the  surface  of  the  ground.  The  entire  sur- 
face must  then  be  thoroughly  broken  with  a  spade  or  plow,  in  order  to 
form  a  bond  with  the  earth  deposited.  Then  a  muck  ditch  must  be  cut  on 
the  river  side  of  the  center  line  :  all  stumps  and  roots  crossing  it  being 
carefully  taken  out  and  removed  beyond  the  base  of  the  levee.  As  each 
section  of  a  mile  in  length  of  the  entire  levee  is  thus  cleared,  broken,  and 
ditch  cut,  the  engineer  sets  the  side  stakes  of  the  base  of  the  levee  ;  the 
muck  ditch  is  then  filled  in  with  buckshot  earth  or  clay  obtained  from 
without  the  base  of  the  levee,  and  the  earth  tamped  in  by  horses  or  mules, 
ridden  rapidly  back  and  forward  constantly  while  the  earth  is  being  put 
in,  or  by  tamping  mauls,  at  least  one  horse  to  every  ten  wheelbarrows,  or 
one  tamping  maul  to  six  wheelbarrows.  This  filling  and  tamping  is  kept 
one-quarter  mile  in  advance  of  the  embankment.  In  case  of  repair  of  old 
levees,  all  stumps,  logs  and  trees,  where  they  are  known  to  exist,  must  be 
dug  out  and  the  muck  ditch  cut  near  the  outside  base  of  the  old  levee,  if 
considered  necessary  by  the  engineer.  The  surface  of  all  old  levees  must 
be  well  broken.  Where  the  chief  constituent  of  the  levee  is  sand,  or  other 
other  porous  material,  the  engineer  may  require  a  wall  of  buckshot  or 
clay,  5  ft.  thick,  to  be  continued  up  from  the  muck  ditch  to  the  top  of  the 
levee,  the  earth  being  tamped  in  by  horses  in  the  same  manner  as  the 
muck  ditch,  as  the  levee  is  built  up  on  each  side  of  it,  the  object  being  to 
obtain  a  stratum  through  the  levee,  impervious  to  "  sipe  water."  If  the 
chief  constituent  of  the  levee  is  stiff  buckshot  or  clay,  the  engineer  may 
require  a  wall  of  sand  8  ft.  thick,  to  be  continued  up  from  the  surface  of 
the  muck-ditch  to  high  water  mark,  as  the  levee  is  built  up  on  each  side 
of  it,  the  object  in  this  case  being  to  obtain  a  perpendicular  stratum 
through  the  levee  impervious  to  crawfish. 

When  the  ground  is  prepared,  the  embankment  will  be  commenced, 
the  slopes  being  commenced  full  out  to  the  side  stakes  and  carried  regu- 
larly up.  The  embankment  must  be  built  one- fifth  higher  than  the  grade 
height  marked  on  the  stakes,  to  allow  for  shrinkage  or  settling. 

Material  is  to  be  obtained  from  places  designated  by  the  engineer,  and 
is  not  to  be  taken  on  the  inside  of  the  levee  except  upon  the  engineer's 
orders.    At  intervals  of  100  ft.  bermes  must  be  left  across  the  borrow  pits 


126  EARTHWORK  AND  MASONRY. 

to  prevent  the  flow  of  a  current  along  the  levee.  All  earth  for  embank- 
ment must  be  entirely  divested  of  roots,  trash  and  other  perishable  mat- 
ter before  being  put  in  place. 

Where  considered  necessary  the  engineer  may  require  a  double  course 
of  sheet  piling,  breaking  joints  to  be  driven  at  the  center  or  either  side  of 
the  levee  5  ft.  below  the  surface  of  the  ground,  and  extending  up  to  within 
6  ins.  of  grade.  The  plant  to  be  of  heart  red  gum,  white  oak  or  cy- 
press, and  of  specified  dimensions.  All  piling  is  driven  in  advance  of  the 
levee,  and  the  embankment  constructed  on  both  sides  of  the  piling  simul- 
taneously. A  breakwater  may  be  constructed  where  necessary  on  the 
river  slope  of  the  levee,  of  post  and  plank  wall,  properly  braced  and  filled 
in  behind  with  earth.  In  anticipation  of  destructive  floods  during  the 
progress  of  the  work,  a  protection  of  timber  work  may  be  constructed 
around  the  ends  of  the  levee,  and  a  temporary  protection  levee  in  front 
of  the  work. 


SPECIFICATIONS  FOR  MASONRY. 

BRICK  FOR  BUILDINGS. 

There  is  not  even  a  remote  approach  to  uniformity  in  the  specifications 
for  the  brick  work  of  buildings.  Ordinarily  the  specifications  for  the 
brick  masonry  are  very  brief  and  incomplete.  The  following  conform 
closely  to  ordinary  construction.  Of  course,  a  higher  gi-ade  of  workman- 
ship can  be  obtained  by  more  stringent  specifications. 

The  brick  in  the  exterior  walls  must  be  of  good  quality,  hard  burned  ; 
fine,  compact  and  uniform  in  texture  ;  regular  in  shape  and  uniform  in 
size.  One  fourth  of  the  brick  in  the  interior  walls  may  be  what  is 
known  as  soft  or  salmon  brick.  The  brick  must  be  thoroughly  wet  be- 
fore being  laid.  The  joints  of  the  exterior  walls  shall  be  from  i  to  f  inch 
thick.  The  joints  of  interior  division  walls  may  be  from  f  to  ^  inch 
thick.  The  mortar  shall  be  composed  of  1  part  of  fresh,  well-slaked  lime 
and  2^  to  3  parts  of  clean,  sharp  sand.  The  lime  paste  and  the  sand 
shall  be  thoroughly  mixed  before  being  used.  The  joints  shall  be  well 
filled  with  the  above  mortar ;  no  grout  shall  be  used  in  the  work.  The 
bond  must  consist  of  five  courses  of  stretchers  to  one  of  headers,  and  shall 
be  so  arranged  as  to  thoroughly  bind  the  exterior  and  interior  portions  of 
the  wall  to  each  other. 

The  contractor  must  furnish,  set  up  and  take  away  his  own  scaffold- 
ing ;  he  must  build  in  such  strips,  plugs,  blocks,  scantling,  etc.,  as  are 
required  for  securing  the  wood  work  ;  and  must  also  assist  in  placing  all 


BRICK  FOR  ARCHES.  187 

iron  work,  as  beams,  stairways,  anchors,  bed  plates,  etc.,  connected  with 
the  brick  work. 

BRICK  FOR  ARCHES. 

The  specifications  for  the  brick  arch  masonry  on  the  Atchison,  Topeka 
and  Santa  Fe  Railroad  are  as  follows: 

"  The  bricks  must  be  of  the  best  quality  of  smooth,  hard  burnt,  paving 
bricks,  well  tempered  and  molded,  of  the  usual  size,  compact,  well 
shaped,  free  from  lime,  cracks  and  other  imperfections,  and  must  stand  a 
pressure  of  4,000  pounds  per  square  inch  without  crushing.  No  bats  will 
be  allowed  in  the  work  except  for  making  necessary  closures.  All  bricks 
will  be  culled  on  the  ground  after  delivery,  and  selected  in  strick  a:;cord- 
ance  with  these  specifications. 

"  The  mortar  must  be  made  of  1  measure  of  good  hydraulic  [Rosendalej 
cement  and  2  measure  of  clean,  sharp  sand— or  such  other  proportion  as 
way  be  prescribed  by  the  engineer  well  mixed  together  with  clean 
mater,  in  clean  motar-beds  constructed  of  boards,  and  must  be  used  im- 
mediately after  being  mixed. 

"  Tiie  brick  must  be  laid  flush  in  cement  mortar,  and  mu8t  be  thoroughly 
wet  when  laid.  All  joints  and  beds  must  b*  thoroughly  filled  with  mortar 
so  as  to  leave  no  empty  spaces  whatever  in  the  masonry  of  the  walls  and 
arches,  which  must  be  solid  throughout.  The  thickness  of  mortar-joints 
must  be  as  follows:  In  the  walls  and  in  the  arch  between  bricks  of  the 
same  ring,  not  less  than  three-eighths  of  an  inch  (f ")  nor  more  than  one- 
half  inch  a").  In  the  arch  between  rings,  not  less  than  one-half  inch  (i") 
nor  more  than  five-eighths  of  an  inch  (f").  Each  brick  is  to  be  driven  into 
place  by  blows  of  a  mallet.  The  bricks  must  be  laid  in  the  walls  with  the 
ordinary  English  bond,  five«stretcher  courses  to  one  header  course.  They 
must  be  laid  in  the  arch  in  concentric  rings,  each  longitudinal  line  of 
bricks  breaking  joints  with  the  adjoining  lines  in  the  same  ring  and  in 
the  ring  under  it.    No  headers  to  be  used  in  the  arch." 

RUBBLE  MASONRY. 

The  following  requirements,  if  properly  complied  with,  will  secure 
what  is  generally  known  among  railroad  engineers  as  superior  rubble: 

Rubble  masonry  shall  consist  of  coursed  rubble  of  good  quality  laid  in 
cement  mortar.  No  stone  shall  be  less  than  six  inches  (6")  in  thickness, 
unless  otherwise  directed  by  the  engineer.  No  stone  shall  measure  less 
than  twelve  inches  (18")  in  its  least  horizontal  dimension,  or  less  than  its 
thickness.  At  least  one-fourth  of  the  stone  in  the  face  shall  be  headers, 
evenly  distributed  throughout  the  wall.    The  stones  shall  be  roughly 


128  EARTHWORK  AND  MASONRY, 

squared  on  joints,  beds  and  faces,  laid  so  as  to  break  joints  and  in  full 
mortar  beds.  All  vertical  spaces  shall  be  flushed  with  good  cement  mor- 
tar and  then  be  packed  full  with  spalls.  No  spalls  will  be  allowed  in  the 
beds.  Selected  stones  shall  be  used  at  all  angles,  and  shall  be  neatly 
pitched  to  true  lines  and  laid  on  hammer-dressed  beds:  draft  lines  may  be 
required  at  the  more  prominent  angles. 

The  top  of  parapet  walls,  piers  and  abutments  shall  be  capped  with 
stones  extending  entirely  across  the  wall,  and  having  a  front  and  end  pro- 
jection of  not  less  than  four  inches  (4").  Coping  stones  shall  be  neatly 
squared,  and  laid  with  joints  of  less  than  one-half  inch  (^  ).  The  steps  of 
wing-walls  shall  be  capped  with  stone  covering  the  entire  step,  and  ex- 
tending at  least  six  inches  (6  )  into  the  wall.  Coping  and  step  stones  shall 
be  roughly  hammer-dressed  on  top,  their  outer  faces  pitched  to  true  lines, 
and  be  of  such  thickness  (not  less  than  six  inches)  and  have  such  projec- 
tions as  the  engineer  may  direct. 

"The specifications  for  rubble  masonry  will  apply  to  rubble  masonry 
laid  dry,  except  as  to  the  use  of  the  mortar." 

Squared-Stone  Masonry. — Squared-stone  masonry  is  employed  for  the 
piers  and  abutments  of  the  lighter  bridges,  for  arches  of  10-foot  span  and 
under,  for  box-culverts,  for  basement  walls,  etc.  The  specifications  are 
usually  about  as  follows: 

The  face  stones  shall  have  quarry  faces  with  edges  pitched  to  a  straight 
line.  Each  stone  shall  be  dressed  to  a  uniform  thickness,  with  beds 
throughout.  No  stone  shall  be  less  than  eight  inches  (8)  thick,  nor 
measure  in  its  smallest  horizontal  dimension  less  than  12  inches  (12  '),  nor 
less  than  its  thickness.  Joints  on  the  face  shall  be  broken  at  least  eight 
inches  (8").  The  bed- joints  and  also  the  vertical  joints  for  eight  inches 
(8")  back  from  the  face  shall  be  dressed  to  one  inch  d").  The  masonry 
need  not  be  laid  up  in  regular  courses,  but  shall  be  well  bonded,  having  at 
least  one  header,  three  feet  (3  .)  long,  to  every  three  stretchers. 

The  stone  shall  be  laid  in  full  cement  mortar  beds,  and  the  joints  shall 
be  packed  full. 

The  backing  shall  consist  of  stone  not  less  than  six  inches  (6")  thick.  At 
least  one-half  of  the  stones  in  the  backing  shall  measure  two  (2)  cubic  feet. 
The  backing  shall  be  laid  in  full  mortar  beds,  and  the  vertical  joints  shall 
also  be  filled  with  mortar.  The  spaces  between  the  large  stones  shall  be 
filled  with  spalls  set  in  mortar. 

The  coping  shall  be  formed  of  large  flat  stones  of  such  thickness  as  the 
engineer  may  direct,  but  in  no  case  to  be  less  than  eight  inches  (8").    The 


ASHLAR  MASONRY.  i39 

upper  surface  of  the  coping  shall  be  bush-hammered,  and  the  joints  and 
beds  shall  be  dressed  to  one  half  an  inch  (i")  throughout.  Each  stone 
must  extend  entirely  across  the  wall  when  the  wall  is  not  more  that  four 
feet  4)  thick. 

ASHLAE  MASONRY. 

The  specifications  for  ashlar,  or  "  first-class  masonry,"  as  employed  on 
railroads,  are  about  as  follows  : 

First-class  masonry  shall  consist  of  quarry-faced  ashlar,  laid  in  regular 
horizontal  courses,  having  parallel  beds  and  vertical  joints  of  not  less  than 
ten  inches  (10")  and  not  more  than  30  inches  (30")  in  thickness,  decreasing 
in  thickness  regularly  from  the  bottona  to  the  top  of  the  wall. 

Stretchers  shall  not  be  less  than  two  and  one-half  feet  (3^')  nor  more 
than  six  feet  (6  )  in  length;  and  not  less  than  one  and  one-half  feet  (1^') 
in  width,  nor  less  in  width  than  one  and  one-fourth  (1^)  times  their 
depth.  Headers  must  not  be  less  than  three  and  one-half  feet  (3J')  in 
length  unless  the  thinness  of  the  wall  necessitates  it,  nor  more  than  four 
and  one-half  feet  m');  and  not  less  than  one  and  one-half  feet  (1|')  in 
width,  nor  less  in  width  than  they  are  in  depth  of  course.  The  beds  and 
sides  of  the  stone  shall  be  cut  before  being  placed  on  the  work,  so  as  to 
form  joints  not  less  than  one-quarter  inch  (I")  and  not  exceeding  five- 
eighths  of  an  inch  (| ")  in  width.  Every  stone  must  be  laid  on  its  natural 
bed,  and  all  stones  must  have  their  beds  well  dressed,  parallel,  and  true 
to  the  proper  line,  and  made  always  as  large  as  the  stone  will  admit. 
The  vertical  joints  of  the  face  must  not  be  less  than  eight  inches  (8")  in 
from  the  face,  and  as  much  more  as  the  stone  will  admit.  All  corners 
and  batter  lines  must  be  built  with  a  neat  chisel-draft  one  and  one-half 
inches  (1^")  on  each  corner.  The  projections  of  the  rock-face  must  not 
exceed  four  inches  (4 ')  beyond  the  draft-lines  of  the  masonry  ;  in  tunnel 
side  walls  this  projection  must  not  exceed  two  inches  (3").  The  masonry 
shall  consist  of  headers  and  stretchers  alternating;  at  least  one  fourth  of 
the  wall  shall  consist  of  headers  extending  entirely  through  the  wall. 
Every  header  shall  be  immediately  over  a  stretcher  of  the  underlying 
course.  The  stones  of  each  course  shall  be  so  arranged  as  to  form  a  proper 
bond  with  the  stones  of  the  underlying  course.  A  bond  of  less  than  one 
foot  (!')  will  in  no  case  be  allowed. 

The  masonry  shall  be  laid  with  cement  mortar  consisting  of  1  volume  of 
cement  of  the  Rosendale  type  and  3  volumes  of  sand.  Each  stone  shall  be 
cleaned  and  dampened  before  being  set.    No  hammering  on  the  wall  will 


130  EARTHWORK  AND  MASONRY. 

be  allowed  after  the  course  is  set ;  but  if  any  inequalities  occur,  they 
must  be  carefully  pointed  off. 

The  backing  shall  be  of  good-sized,  well-shaped  stones,  laid  so  as  to 
break  joints  and  thoroughly  bond  the  work  in  all  directions  and  leave  no 
spaces  between  them  over  six  inches  (tt  )  wide,  which  spaces  shall  be  filled 
with  small  stones  and  spalls  set  in  cement  mortar. 

All  foundation  courses  must  be  laid  with  selected,  large,  flat  stones  not 
less  than  twelve  inches  (12")  in  thickness,  nor  of  less  superficial  surface 
than  fifteen  (15)  square  feet. 

The  coping  shall  be  formed  of  large  flat  stones,  which  shall  extend  en- 
tirely across  the  wall  when  the  same  is  not  more  than  six  feet  (6)  wide. 
The  steps  of  wing  walls  shall  be  capped  with  stone  covering  the  entire 
step  and  extending  under  the  step  next  above  at  least  twelve  inches  (1^"). 
Coping  and  step  stones  shall  be  at  lease  twelve  inches  (12")  thick,  and 
have  such  projections  as  the  engineer  may  direct  (usually  3  to  6  inches). 
The  tops  and  faces  of  copings  ar.d  step  stones  shall  be  bush-hammered 
and  their  joints  and  beds  cut  to  one  quarter  inch  (i")  throughout. 


CHAPTER  VII. 


Culverts  and  Bridges. 

STANDARD  TIMBER  BOX  CULVERTS. 
Reprinted  from  the  Railroad  Gazette. 

There  is  a  strong  feeling  among  engineers,  which  finds  expression  in 
the  construction  of  nearly  all  lines  on  which  timber  is  used  at  all,  that  the 
use  of  timber  box  culverts  is  bad  practice  ;  that  where  the  fill  is  not  over 
6  or  8  feet  high — or  sometimes  even  10  feet  high — open  timber  culverts 
should  be  used  instead,  and  where  the  fill  is  too  great  for  such  open  cul- 
verts, pile  or  timber  trestles  should  be  used,  or  else  masonry.  The  prac- 
tice of  the  Chicago,  Milwaukee  &  St.  Paul  is  different  from  this,  on  all 
the  thousands  of  miles  which  it  has  built  or  is  building,  where  stone  can- 
not be  obtained  at  all,  or  only  with  much  difficulty  and  cost.  In  such 
cases,  the  rule  on  that  line,  even  in  timber  work,  is  never  to  use  an  open 
culvert  when  timber  can  be  used  instead.  In  this  it  is  not  alone,  but  we 
believe  it  is  fairly  entitled  to  the  credit  of  having  set  the  fashion,  which  Is 
not  yet  a  very  general  fashion. 

It  is  defended  by  the  following  argument:  That  though  it  is  true  that 
the  wood  decays,  and  though  it  is  true  that  there  is  somewhat  less  cer- 
tainty of  knowing  of  dangerous  decay  in  advance,  yet  it  is  not  true  that 
decay  is  more  rapid  than  with  open  structures,  nor  that  they  are  as  likely 
to  give  way  when  they  are  decayed,  nor  that  the  consequences  are  likely 
to  be  so  serious  if  they  do  give  way.  In  the  meantime  the  average  con- 
dition of  a  poorly  ballasted  or  wholly  unballasted  track  is  very  much 
better  than  with  open  structures. 

Therefore,  the  practice  on  that  line  is  to  use  timber  box  culverts 
wherever  possible,  to  have  them  inspected  periodically  and  carefully,  and 
whenever  their  condition  demands  it  and  convenience  serves,  to  renew 
them,  not  with  stone  but,  as  a  rule,  with  iron  pipes.  It  is  not  found  in 
practice,  however,  that  even  a  considerable  amount  of  decay  endangers 
caving  in  of  the  bank  greatly,  especially  when  the  bank  is  of  some  con- 
siderable height.  After  the  bank  has  once  become  solid,  on  the  contrary, 
which  of  course  is  long  before  the  timber  begins  to  decay  seriously,  it  is 


132 


CULVERTS  AND  BRIDGES. 


Side  Tipitters  to  1)6  Drift  BolteS  toi^ther  every'6  ft. 
^p^/  withX'x20'Drifts_^.^ 

<VV^  6'Covering  °    "-""""• 


Side  Timbers,  8  x  12' 

S'x  12'SlU».i»<  mow  thin  l^SJS  8  ft  CentretoCeMre  SiS  Nyru— Tte  two  Tlmb«r  Colvctta  ■wffli   opcSing  of 
I  .v^,/M.i-iirM>i'.i    ___—,-M,3'4"and4'S'are  to  be  used  only  when  B»nk  l«  too  low 
1.0NGITUDINAL  SECTION  ^^  ^j^,,  ^f  j^^  gquare  Form,  witU  not  lew  than  ftlncia 
of  earth  on  top  of  Covering. 

Two-TiMBEB  Culverts. 


•V  Side  TimTjerfftoW  Drift  Bolted  together  every  6  ft. 
J.^P>  with  ^y  20'Dri  f t« 

vJ^'Co 


e'xl2'8UltA(it.mw«.tlun^^    8  rCcutn  to' 

longitudinal  sktion 
Three-Timber  Culverts. 


<i^Ide  TliMberffto  IbeDrift  Bolted  together  every  6  A  ■ 

^•^  with  '^"x  20'Drift3  inTi«.,„w 

•"Vs-coverino-        _      __£Cov£tl2g_  -  10  Cohering 


»  ft.  Ctntre  to  Centn  SS  t=^ 

longitudinal  section 
Four-Timber  Culverts. 


\  Side  !Binlj«a«  to  be  Drift  Bolted  together  ereiT  «  A 

^X>:  with  ^  X  aO'Drifts  ■m-r.-^v-v Mn,» 

NTS'i  Coverine  s'Coverinp  ^      _  10  Covering 


r^rerj  SUth  SUck  S'lbicki    \    Eierj  Sixth  Slick  Notched  2 


^    ^         Side  Timbers,      > 


8  (L  Centre  {olSntra  t 

longitudinal  section 
Four  Timber  Double  Culverts. 


Standard  Timber  Box  Culverts,— Chicago,  Milwaukee  &  St,  Paul  Ry. 


STANDARD  TIMBER  BOX  CULVERTS. 


Covcrinfe  I^Thlck,  for  M 
Jietglits  of  Banlu 


^s'^si- 


Corerlnc  sTUlcIc,  {or  dl 

Helcbts  of  Bulls 

44 tiSi 4- 


m     8Pl»nt.  ^ 

I  rfeuic-Ti^r«'-(n  I 


Buk.  Ctrnrimg 

Orar  !&  (1.     8  iDobu 


Beltftor      TbleVOMtvf 
V*Bk(  CoTerinf. 


Bclchtof'      Thiefaiewof 

Bttok.  *  CoreriD^ 

Vf  U  25  ft     t  lochu 


Helii&tat  tUatoMMof 

£uik  CoTcrinf. 

Up  W 15  fL  «  InehM 

UfttoS&ft.  aineliu 
.OT«r25fl.. 


SPlanV 

I  r"ysiir?7igi'i}^"i"]  i  c 


Btl|bto(       nieViMM  •( 
BuilL  CoTCrijlf. 

AU  tlnAcf 


Bdglit  of       ThklnwK  of 

Up  to  S^.ft.     fi  iBchct 
Orer  26  (i:     8  iaohct 


7U(htof  TUdcBCMoC 

fiAnk.  Corcrtn^ 

rp  to  IS  ft  « liicliM 

Utto2Sfti  Slnokot 

■VniHtt.  .tOlnolM* 


mt~ ^■'^ *fl?T *C^ ^121  »12t)« ^' f^if -SV >|12' 

standard  Timber  Box  Culverts. — Chicago,  Milwaukee  &  St,  Paul  Ry. 


1 34  CULVERTS  AND  BRIDGES. 

found  that  they  very  seldom  cave  in,  and  that  in  putting  in  the  iron  pipe 
the  timber  may  be  almost  completely  cut  away  at  top,  bottom  and  sides 
for  the  insertion  of  circular  pipes  without  danger;  a  safe  indication  for 
the  workmen  being  that  wherever  the  timber  is  punky  and  rotten  there 
can  be  no  immediate  danger  in  removing  it  altogether,  and  after  the 
expiration  of  very  much  less  than  15  to  20  years,  which  is  no  unusual 
time  for  these  culverts  to  remain  in  service,  all  the  interior  of  the  wood 
at  least  where  it  is  exposed  to  the  air,  is  pretty  sure  to  be  punky  and 
rotten,  its  chief  and  all-sufficient  function  seeming  to  be  to  sustain  the 
pressure  of  earth  during  the  process  of  solidification  only,  and  thereafter 
chiefly  to  protect  the  interior  surface  of  the  earth  fill  from  the  influence 
of  the  atmosphere,  which  alone  suffices  to  restrain  all  considerable  ten- 
dency to  cave. 

It  follows  that  the  size  of  the  iron  pipes  which  are  ordinarily  used  for 
renewal,  when  it  is  not  clearly  safe  to  use  a  smaller  pipe,  will  be  given 
by  determining  with  a  pair  of  dividers  the  largest  circle  which  can  be 
drawn  within  the  exterior  limits  of  the  culvert  walls  without  cutting 
away  more  than  half  or  two-thirds  of  the  thickness  of  the  wood  at  top  or 
sides  at  any  point,  the  greatest  liberties  being  taken  of  course  with  bot- 
tom timbers.  In  doing  this,  the  first  section  of  the  pipes  is  entered  at 
one  end  and  drawn  clear  through  to  the  other  end  by  appropriate  tackle, 
the  workmen  clearing  away  in  advance  of  it.  After  the  first  pipe  has 
been  drawn  through  and  placed  in  position,  the  following  pipes  are 
drawn  up  to  it  in  succession,  one  after  another,  very  speedily,  and  the 
whole  work  is  complete.  A  masonry  end  nmy  or  may  not  be  added.  The 
pipes  used  range  from  24  to  60  in.  in  diameter,  and  are  cas-t  at  the  com- 
pany's foundry  of  any  scrap  which  comes  convenient.  They  are  provided 
with  a  simple  bell  mouth  large  enough  merely  to  hold  the  pipes  in  line 
with  each  other  without  any  attempt  at  calking. 

The  sizes  of  pipe  used,  of  course,  depend  largely  on  what  has  proved  to 
be  the  requirements  of  the  water  way.  "When  the  culvert  has  been  in 
Tise  some  years  the  presumption  is  fair  that  no  larger  water  way  than  be- 
fore is  necessary,  and  this,  or  even  more,  is  readily  obtained  by  pipes  in 
the  manner  described. 

Whether  or  not  this  manner  of  using  and  renewing  wood  is  good  and 
safe  practice  is  simply  a  matter  of  experience.  Experience  in  almost  all 
kinds  of  soil  appears  to  indicate  that  it  is,  a  notal.le  advantage  being  that 
in  the  rare  cases  where  culverts  cave  in  they  do  not,  as  a  rule,  produce  a 
dangerous  disturbance  of  the  surface,  whereas  if  an  open  culvert  or  tres- 


MAX  IMUM  SPAN  S  OF  STONE  BOX  CULVERTS.  136 

tie  has  been  carelessly  allowed  to  become  too  weak,  an  accident  is  almost 
certain,  while  it  is  almost  impossible  to  make  a  new  track  with  many 
open  structures  in  it  ride  even  fairly  well. 

There  is  perhaps  no  detail  of  American  practice  m  which  foreign  critics, 
accustomed  to  new  lines  made  thoroughly  solid  and  complete  before  they 
are  allowed  to  be  opened,  are  more  apt  to  comment  unfavorably  than  on 
the  practice  of  opening  first  with  temporary  works,  and  completing  with 
permanent  works  afterwards,  which  may  be  called  the  standard  Ameri- 
can practice.    Yet  there  is  much  to  be  said  for  it. 

There  are  three  other  considerations  of  great  weight: 

Firht.—Jhe  exact  requirements  of  the  locality  become  better  known, 
and  costly  and  dangerous  mistakes  may  be  more  fully  avoided. 

Second. — The  work  can  be  prosecuted  in  a  more  leisurely  manner  and  at 
more  appropriate  seasons,  and  thus  greater  durability  insured. 

Third. — The  work  can  be  prosecuted  more  cheaply,  there  being  the 
advantage  of  locomotive  power  for  delivering  stone,  cement  and  iron 
work  and  for  making  fills  by  trains  ;  often  at  but  a  fraction  of  the  cost  of 
executing  the  permanent  work  in  advance  of  these  facilities. 

As  for  safety,  there  is  no  question  but  that  wooden  structures,  properly 
designed  and  properly  watched  and  renewed,  are  entirely  safe,  and  the 
thing  to  be  protested  against,  therefore,  is  lack  of  care  and  skill  in  using 
them  and  not  the  things  themselves.  The  difference  in  the  cost  of  a  good 
and  of  a  bad  wooden  structure  is  not  so  good  that  there  is  ever  any  excuse 
for  the  latter,  though  it  must  be  admitted  that  they  are  far  from  un- 
known. 

For  these  reasons  there  is  no  apology  demanded  for  the  reasonable  and 
cautious  use  of  the  practice  of  "  opening  roads  first  and  building  them 
afterwards,"  as  it  has  been  called,  even  when,  as  on  the  Chicago,  Milwau- 
kee &  St.  Paul  and  thousands  of  miles  of  other  road  in  the  West,  the  use 
of  stone  structures  for  opening  the  road  is  wholly  out  of  the  question. 

MAXIMUM  SPANS  OF  STONE  BOX  CULVERTS. 

BY  EMILE  LOW,   C.  E. 

The  table  given  below  shows  the  maximum  span  or  horizontal  inside 
opening  of  box  culverts,  having  covering  stones  of  good  sandstone,  vary- 
ing in  thickness  from  six  (8)  to  eighteen  (1«)  inches,  and  being  under  em- 
bankments of  from  four  (4)  to  one  hundred  (100)  feet  in  height. 

The  table  has  been  calculated  for  an  earth  embankment,  the  weight  of 
a  cubic  foot  of  earth  having  been  taken  at  eighty  (80)  pounds. 


136  CULVERTS  AND  BRIDGES, 

Should  the  embankment  be  made  of  heavier  material,  such  as  rock,  a 
reduction  of  the  span  must  then  be  made. 

The  ultimate  tensile  strength  of  the  stone  has  been  taken  at  eight  hun- 
dred and  sixty  four  (864)  pounds  per  square  inch,  but  one-tenth  of  that, 
or  eighty-six  and  four-tenths  (86  4-10)  pounds  per  square  inch,  has  been 
used  in  the  calculation  of  the  tables. 

The  for-mula  used  is  as  follows: 

in  which 
1   =  clear  span  in  feet. 
c  =  depth  of  covering  stone  in  inches. 
H  =  height  of  earth  embankment  over  covering  stone  in  feet. 


Height  of 

Span  of  Box 

Culverts  with  coverine  stone. 

embankment. 

ihe  following  depth  in  inches. 

6" 

9" 

12" 

15" 

18" 

4 

3.60 

5.40 

7.20 

9.00 

10.80 

9 

2.40 

3.60 

4.80 

6  00 

7.20 

16 

1.80 

2.70 

3.60 

4.50 

5.40 

25 

1.44 

2.16 

2.88 

3.60 

4.32 

36 

1.80 

2.40 

3.00 

3.60 

49 

.... 

2.06 

2.57 

3.09 

64 

.... 

.... 

1.80 

2.25 

2.70 

81 

2.00 

2.40 

luO 

.... 

2.16 

I  also  append  a  table  showing  the  weight  of  the  superincumbent  em- 
bankment (taken  at  80  pounds  per  cubic  foot),  for  the  length  of  one  (1)  foot 
of  the  same  in  the  direction  of  the  axis  of  the  culvert  and  in  width  equal 
to  the  spans  as  given  above  for  the  different  heights  of  embankments. 

Height  of  Weight  of  Embankment  in  pounds  per  lineal  foot  of  Culvert 

embankment.  and  for  widths  as  per  table  at)ove. 

4  1152                 1728                 2304  2880  3456 

9  1728                 2592                 3456  4320  5184 

16  2304                  3456                 4608  5760  6912 

25  2880                 4320                5760  7200  8610 

38  ....                  6184                 6912  8640  10368 

49  ....                  ....                  8064  10080  12096 

64  ....                  .  ..                 9216  11520  13324 

81  ....                  ....                  ....  12960  15552 

100  ....                  ....                 ....  ....  17280 


SPECIFICATIONS  FOR  STONE  BOX  CULVERTS.* 
All  stone  box  culverts  shall  have  a  water  way  at  least  2-J  X  3  feet.   The 
side  walls  shall  not  be  less  than  two  feet  (2)  thick,  and  shall  be  built  of 

'Pennsylvania  Railroad. 


SPECIFICATIONS  FOR  STONE  ARCH  CULVERTS.  187 

sound,  durable  Stones  not  less  than  six  Inches  (6")  thick,  laid  in  cement 
mortar  [usually  1  part  Rosendale  cement  to  2  parts  sand].  The  walls 
must  be  laid  in  true  horizontal  courses,  but  in  case  the  thickness  of  the 
course  is  greater  than  12  inches  (12"),  occasionally  two  stones  may  be  used 
to  make  up  the  thickness.  The  walls  must  be  laid  so  as  to  be  thoroughly 
bonded,  and  at  least  one  fourth  of  the  area  of  each  course  must  be  headers 
going  entirely  through  the  wall.  The  top  course  must  have  one-half  its 
area  of  through  stones,  and  the  remainder  of  this  course  must  consist  of 
stone  going  at  least  one-half  of  the  way  across  the  wall  from  the  inside 
face.  The  face  stone  of  each  course  must  be  dressed  to  a  straight  edge, 
and  pitched  off  to  a  true  line.  All  of  the  coping  stones  of  head  walls 
must  be  throughs,  and  must  have  the  upper  surface  hammer-dressed  to  a 
straight  edge,  and  the  face  pitched  off  to  a  line  with  margin  dralt. 
Cover  stones  shall  have  a  thickness  of  at  least  twelve  inches  (12")  for 
opening  of  three  feet  (3),  and  at  least  14  inches  (14")  for  opening  of  four 
feet  (4);  and  must  be  carefully  selected,  and  must  be  of  such  length  as  to 
have  a  bearing  of  at  least  one  foot(10  on  either  wall. 

The  beds  and  vertical  joints  of  the  face  stones  for  a  distance  of  six 
inches  (6)  from  the  face  of  the  wall  shall  be  so  dressed  as  to  require  a 
mortar  joint  not  thicker  than  three  fourths  of  an  inch  (f").  Joints  be- 
tween the  covering  stones  must  be  not  wider  than  three-fourths  of  an 
inch  (%"),  and  the  bearing  surface  of  cover  stones  upon  side  walls  must  be 
so  dressed  as  to  require  not  more  than  a  one-inch  (1")  mortar  joint. 

The  paving  shall  consist  of  flat  stones,  set  on  edge,  at  right  angles  with 
the  line  of  the  culvert,  not  less  than  twelve  inches  (12")  deep,  and  shall  be 
laid  in  cement  mortar  and  grouted. 


SPECIFICATIONS  FOR  STONE  ARCH  CULVERTS.* 

Foundations. — "  When  the  bottom  of  the  pit  is  common  earth,  gravel, 
etc.,  the  foundations  of  arch  culverts  will  generally  consist  of  a  pavement 
formed  of  stone,  not  less  than  twelve  inches  (12")  in  depth,  set  edgewise, 
and  secured  at  the  ends  by  deep  curbstones  which  must  be  protected  from 
undermining  by  broken  stone  placed  in  such  quantity  and  position  as  the 
engineer  may  direct.  When  the  bottom  upon  which  a  culvert  is  to  be 
built  is  soft  and  compressible,  and  where  it  will  at  all  times  be  covered 
with  water,  timber  well  hewn,  and  from  eight  (8")  to  twelve  inches  (12") 
in  thickness,  according  to  the  span  of  the  culvert,  shall  be  laid  side  by  side 

*  Pennsylvania  Railroad. 


138  CULVERTS  AND  BRIDGES. 

crosswise  upon  longitudinal  sills;  and  when  the  position  of  the  culvert  is 
such  that  a  strong  current  will  be  forced  through  during  floods,  three 
courses  of  sheet  piling  shall  be  placed  across  the  foundation,  one  course  at 
each  end,  and  one  in  the  middle, — which  shall  be  sunk  from  three  (3)  to 
six  (6)  below  the  top  of  the  timber,  according  as  the  earth  is  more  or  less 
compact," 

First-Class  Arch  Masonry. — "  First-class  arch  masonry  shall  be  built 
in  accordance  with  the  specifications  for  first-class  masonry  *[j^"385],  with 
the  exception  of  the  arch  sheeting  and  the  ring  stones.  The  ring  stones 
shall  be  dressed  to  such  shape  as  the  engineer  shall  direct.  The  ring  stones 
and  the  arch  sheeting  shall  be  of  stone  not  less  than  10  inches  (10)  thick 
*on  the  intrados,  shall  be  dressed  with  three-eighths  of  an  inch  (f ")  joints, 
and  shall  be  of  the  full  depth  specified  for  the  thickness  of  the  arch;  and 
the  joints  shall  be  at  right  angles  to  the  surface  of  the  intrados.  The  face 
of  sheeting  stones  shall  be  dressed  to  make  a  close  centering  joint.  The 
ring  stones  and  the  sheeting  shall  break  joints  not  less  than  one  foot  (1 ). 

"The  wings  shall  be  neatly  stepped  with  selected  stones  of  the  full 
width  of  the  wing  and  of  not  less  than  ten  inches  (10")  in  thickness,  which 
shall  overlap  by  not  less  than  eighteen  inches  (18"),  or  shall  be  finished 
with  a  neatly  capped  newel  at  the  free  end,  and  a  coping  course  on  the 
wing.  The  parapets  shall  be  finished  with  a  coping  course  not  less  than 
ten  inches  (10")  thick  and  of  the  full  width  of  the  parapet,  which  shall 
project  six  inches  (6")." 

Second-Class  Arch  Masonry.—''  Second-class  arch  masonry  is  the  same 
as  second-class  masonry,  with  the  exception  of  the  arch  sheeting.  The 
stones  of  the  arch  sheeting  shall  have  a  good  bearing  throughout,  and 
shall  be  well  bonded  and  of  the  full  depth  of  the  thickness  of  the  arch. 
No  stone  shall  less  than  four  inches  (4")  in  thickness  on  the  intrados. 
Ring  stones  of  all  arches  over  eight  feet  (8  )  span  shall  be  dressed  accord- 
mg  to  specifications  for  first-class  arch  masonry." 


Baker's  Masonry  Construction. 


HOWE  TRUSS  BRIDGES. 


139 


HOWE  TRUSS  BRIDGES . 

In  Engineering  News  of  April  26,  1890,  a  double  page  lithographed 
inset  was  published,  showing  37  strain  sheets  and  sizes  of  members  for 
Howe  truss  bridges  from  80  feet  to  150  feet  span,  sent  by  Chief  Engineer 
A.  A.  Schenck,  of  the  Oregon  Pacific  Railway  Co.,  and  which  we  believe 
to  be  safe  and  careful  designs,  in  accordance  with  the  latest  and  best 
practice  in  wooden  bridge  construction,  which  for  a  long  time  to  come 
will  be  an  important  department  of  American  engineering  work,  although 
one  of  continually  decreasing  relative  importance. 

One  fact  we  should  especially  call  attention  to,  that  these  bridges  are 
designed  for  a  region  where  very  long  timber  is  readily  obtained,  and  is 
no  more  expensive  than  short  timbers,  so  that  the  sections  given  for  lower 
chord  would  be  much  weaker  in  proportion  to  regions  where  equally  long 
timber  was  not  available.  The  great  difference  in  the  amount  of  iron 
required  when  the  rods  are  upset  or  not  upset,  is  curiously  shown  in  the 
table  of  data  herewith  reprinted-. 


Table  of  Data. 


No.  of  Span. 


1. 
2. 
3. 

4. 

5. 

6. 

7, 

8. 

9, 
10 
11 
12 
13. 
14 
15, 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 


Assumed  loading 
per  foot. 


360 

360 

400 

•   400 

450 

450 

540 

540 

600 

600 

620 

620 

720 

720 

720 

800 

800 

880 

880 

940 

940 

1,000 

1.000 

1,050 

1,050 

1,100 

1,100 


2  -^ 


500 


5.060 
5.060 
4.600 
4,600 
4,200 
4,200 
3,860 
3,860 
3.610 
3,640 
3,600 
3,600 
3,560 
3,560 
3,560 
3.500 
3,500 
3,400 
3,400 
3,300 
3,300 
3,200 
3,200 
3,150 
3,150 
3,100 
3,100 


5.620 
5,920 
6.600 
6,500 
5,150 
5,150 
4,900 
4,900 
4,740 
4,740 
4,720 
4.720 
4.780 
4,780 
4,780 
4,8C0 
4,800 
4,780 
4,780 
4,740 
4,740 
4,70.) 
4,700 
4,700 
4,700 
4,700 
4,700 


Estimate  of  Quantities. 


10,165 
6,750 
13,358 
9,362 
19,025 
12,861 
22,786 
20.702 
29,931 
27,617 
35,388 
32,764 
42,709 
41,883 
40,690 
48,892 
46,454 
54,767 
50,295 
62,038 
59,254 
70,128 
66,779 
78,156 
76,323 
86.632 
86,053 


£  00 


2,170 

1,930 

2.960 

3,280 

5,610 

4,710 

6,790 

5,900 

9,260 

8,420 

11660 

10,190 

15,170 

17,880 

13,220 

22,.580 

18.040 

25,820 

19,400 

30,890 

23,080 

37,050 

27,930 

40,820 

32.640 

48,090 

39,630 


a 

I4  00 


.970 

1.210 

1,070 

1,550 

2.880 

2,830 

3,660 

3,8.S0 

8.260 

7,980 

9,790 

9,730 

12,530 

12,260 

12,710 

14,290 

13,990 

15,930 

14,050 

18,g90 

16,520 

20,830 

20,460 

23,210 

23,260 

27,060 

27,140 


8,210 
7,610 
10,260 
9,120 
13,440 
16,150 
11,820 
18,950 
16,040 
22,290 
16,320 
26.010 
19,580 
30,180 
23,560 
33,020 
27,360 
39,140 
33,390 


140 


CULVERTS  AND  BRIDGES. 


Strains  given  are  for  one  truss,  and  in  1,000  pounds. 

Sections  given  are  for  one  trass  (rods  assumed  not  upset). 

Loads  in  above  table  are  for  two  trusses. 

Strains  are  those  due  to  dead  load  -j-  maximum  from  moving  load. 

Assumed  live  loads  are  intended  to  fully  equal  (in  strains  produced)  those  given 
in  diagram  below. 

Load  on  a  floor  beam,  14,000  pounds,  on  a  panellength  of  chord  as  a  beam;  36,C00 
pounds  on  an  axle. 

Wrought  iron  in  tension.  10,000  pounds  (net  section  at  root  of  thread)  per 
square  inch . 

Wood  (in  compression  only)  1-6  to  1-8  of  breaking  load  by  Smith's  formula. 

Wood  (in  tension  only)  usually  800  pounds  to  l.i  0)  pounds,  (500  pounds  to  800  pounds 
in  shortest  span),  per  square  inch;  and  as  packed  beam  maximum  section  (net  sec- 
tion) 800  tc  1,000  pounds, 

LATERAL  SYSTEMS. 

De;k  Spans— a  uniform  load  of  150  pounds  per  foot  (each  system),  }4  of  it  at  feet 
of  rods. 

A  moving  load  of  150  pounds  per  foot  (each  system),  all  of  it  at  feet  of  rods. 

Sway  braces  at  each  panel  assumed  to  equalize  the  strains  so  that  each  system  is 
the  same  (except  end  rods). 

Through  Spans— A  uniform  load  of  150  pounds  to  200  pounds  per  foot  (each  sys- 
tem).   A  moving  load  of  300  pounds  per  toot  (lower  system). 

Iron  13,000  to  15,000  pounds  per  square  inch  net.    Timber  1-4  to  1-5  breaking  load. 

The  spans  inclu(3ed  in  the  dia^ams  are  : 


30  ft.  half -through  and  deck. 

40 

50 

60 

70 

80 


100  ft.  through,  and  deck. 
110  " 
120  '• 
13G  " 
140  " 
I  150  •' 


90  "  through,  half-through  and  deck.       | 

This  includes  in  all  37  different  trusses,  covering  the  entire  range 
usually  required  for  wooden  trusses,  spans  exceeding  150  feet  being  rare- 
ly built  of  wood. 

In  a  letter  transmitting  these  strain  sheets,  Mr.  W.  A.  Doane,  M.  Am. 
Soc.  C.  E.,  gives  the  following  further  details: 


Fig.  1.    Top  Chord  End  Joints  for  Howe  Tniss  Spans  up  to  90  ft. 


HOWE  TRUSS  BRIDGES, 


141 


•'  Howe  truss  bridges,  not  yet  having  had  their  day — at  least  in  the 
South  and  West—  I  send  you  a  set  of  strain  sheets  from  30  feet  to  150  feet 
spans,  designed  for  heavy  traflSc.  They  require  little  explanation  be- 
yond that  given  by  tke  attached  notes  and  table  of  data. 

It  is  intended  to  use  upset  rods  for  all  spans  above  60  or  70  feet,  although 
diameters  given  are  those  required  to  give  the  necessary  area  at  root  of 
thread.  The  table  of  data  gives  approximate  weights  in  each  case.  As 
will  be  seen,  from  1,000  to  9,000  pounds  of  iron  per  span  are  saved  by  up- 
setting the  ends  of  rods. 

It  is  believed  that  some  details  of  construction  have  been  improved  in 
these  designs. 

"  Fig.  1  (enlarged  scale)  shows  the  general  style  of  joints  at  junction  of 
top  chord  with  end  mains  for  all  through  spans  up  to  90  feet. 


Fig.  3.    Portal  Bracing  for  Howe  Truss  Through  Spans  of  90  ft. 

and  over. 


142 


CULVERTS  AND  BRIDGES. 


"  Fig.  3  shows  general  style  of  portal  bracing,  etc.,  for  through  spans 
over  90  feet,  these  having  a  system  of  top  lateral  bracing.  In  no  case  are 
vertical  end  posts  used  to  meet  a  useless  prolongation  of  top  chord  in 
through  spans. 

"  For  spans  of  100  feet  and  over,  the  usual  style  of  cast  brace  blocks  is 
followed,  having  tubes  shghtly  let  in  to  chord  timbers  and  long  enough 
to  reach  the  opposite  face  of  chord  and  receive  the  strain  transmitted 
from  the  rods  through  the  plates.  These  latter  are  in  all  cases  made  un- 
usually wide,  however, 

"  In  spans  less  than  100  feet  the  tubes  are  dispensed  with,  and  a  block 
of  the  style  shown  in  Fig.  2  is  used,  having  a  full  bearing  on  the  chord 
as  well  as  for  the  braces,  while  the  radial  longitudinal  ribs  greatly  in- 
crease the  strength.    The  open  ends  are  not  objectionable." 


Fig.  2.    Cast  Brace-Block  for  Howe  Truss  Spans  under  100  ft. 

It  was  not  practicable  to  reproduce  the  sheet  of  diagrams  for  this  book. 
The  reader  who  wishes  to  post  himself  on  the  best  practice  in  Howe  truss 
construction  can  consult  the  number  of  the  journal  in  which  the  diagrams 
are  pubhshed. 


COST  OP  ERECTING  A  WOODEN  HOWE  TRUSS  BRIDGE.  143 


COST  OF  LABOR  IN  FRAMING  AND  ERECTING  A  WOODEN  HOWE 
TRUSS  BRIDGE. 

We  have  had  sent  to  us  a  very  full  and  careful  set  of  notes,  detailing 
the  actual  cost  for  labor  of  framing  and  erecting  five  spans  of  150  ft. 
each,  of  a  wooden  arched  Howe  truss  bridge,  built  by  one  of  the  best 
known  firms  in  the  country.  We  give  an  abstract  of  these  for  the  benefit 
of  any  whom  it  may  concern.  The  general  dimensions  of  the  bridge  were 
as  follows : 

Number  of  spans 5 

Numberof  trusses  to  each  span 2 

Number  of  arches  I o  each  truss 2 

Length  of  truss,  c  to  c,  of  end  angle-blocks 149  ft.  4  in. 

Length  of  panel  over  pier 2  ft.  Sin. 

Number  of  panels  in  each  truss 14 

Lentjth  of  each  panel  10  ft.  8  in . 

Proiectionof  chords  beyond  centre  of  end  angle-block 2  ft. 

Height  of  truss  between  chords 20  ft. 

Depth  of  lower  chord 14  in. 

Depth  of  upper  chord      12in. 

Widthof  chord 2ft.3in. 

Depth  of  arches  (3  pieces,  8  in.  X  9  in.,  1  in.spaces)    .  2ft,5in. 

Width  of  arches •. 8  in. 

Width  of  bridge  in  clear  between  trusses 19  ft.  4  in. 

Width  of  bridge  in  clear  between  arches 18  ft. 

Radius  of  upper  line  of  arch 108  ft.  4  in. 

Length  of  bridge  centres  of  end  angle-blocks 757ft.4in. 

The  wages  paid  were  as  follows:  Foreman,  $3.60  per  day;  carpenters, 
$3.75;  helpers,  $2.25,  and  laborers,  $1.85.  Work  was  commenced  in  Octo- 
ber, 1873,  and  continued  without  interruption  thereafter  until  July,  1874. 
when  the  bridge  was  completed. 

The  cost  of  the  work  may  be  itemized  as  follows  : 

Framing  arches,  cost f49o.31 

Painting  arches,    "    29.70 

Total $525.01  or  66o.  per  lin.  ft.  bridge. 

Framing  trusses,  cost ^.002.62  or  $2.64  " 

Painting  daps,  etc.,  cost 105.70  or  14c.     "       '*  " 

Framing  thefalse  works,  making  "  balance  beams  "  for  raising,  making 

a  flat  and  preparing  generally  for  the  erection  of  bridges  cost  as  follows  : 

Framing  false  works $57.96 

Preparing  for  raising 173.98 

Painting  iron 42.75 

Total $274.69 

Time  consumed  in  framing  false  works,  3 J  days'  work  of  7  men. 

The  cost  of  raising — for  one  foreman  and   19  men,  working  79  days,  in- 


144  CULVERTS  AND  BRIDGES. 

eluding  a  bill  of  $220.61  for  watchman,  horse,  blacksmithing  and  expen- 
ses— was  $2,989.45;  reduced  to  cost  per  lin.  ft.  of  bridge  this  amounted  to: 

False  works $57  96  or  $0.08  per  lin.  ft.  bridge. 

Paintingiron 103.65  or    0.14       "         "       " 

Raising  bridge 2,989.15or    3.94       "  "       " 

Or  to  summarize  under  the  following  general  heads,  the 

Framing  cost $2,603.63  or  $3.44  per  lin.  ft.  of  bridge. 

Kaisingcost 3,151.06or    4.16 

Totalcost $5,754.69  "  $7.60       

The  cost  of  lumber  and  iron  is,  of  course,  not  included  in  the  above  ac- 
count, which  simply  covers  the  labor. — Erigineering  News,  March  24,  1883. 


HOWE  TRUSSES  ON  THE  CANADIAN  PACIFIC  RAILWAY. 


The  Howe  trusses  nearly  all  have  the  following  floor  :  Guard  rails,  8  in. 
X  8  in.,  sized  to  6i  in.  at  ties,  placed  10  ft.  6  in.  apart  in  the  clear,  bolted 
through  the  tie  and  outside  stringer  by  f-iu.  bolts  (|  in.  X  3^  in.  cast 
washers) ;  ties  8  in.  X  8  in.,  12  ft.  long,  spaced  16  in.  centres  ;  every  5  ft. 
4  in.,  or  every  fourth  tie  guard  rail,  tie  and  stringer  bolted.  The  ties  are 
sized  to  7i  in.  at  the  stringers  on  some  bridges.    Six  lines  of  stringers,  all 

8  in.  X  10  in.,  two  under  eachrail,  breaking  joints  and  packed  3  in.  apart. 
Packing  bolts  f  in.  (about  5  ft.  apart).  The  other  four  stringers  are  under 
the  guard  rails.  In  each  panel  there  are  four  f-in.  bolts  through  one  of 
the  stringers  and  floor  beam.     The  floor  beams  vary  from  6  in.  x  15  in.  to 

9  in.  X  15  in.  ;  4  to  5  per  panel,  bolted  through  the  chord  by  f-in.  bolts. 
All  through  bridges  are  15  ft.  wide  in  clear,  and,  where  the  top  lateral 

bracing  is  used,  are  about  21  ft.  from  top  of  rail  to  bottom  of  braces. 

The  dead  load  is  generally  10^  greater  than  given  by  TRAUTWINE  for 
the  trusses,  and  400  to  650  lbs.  per  ft.  for  the  floor. 

lion  in  tension  is  strained  not  to  exceed  10,000  lbs.  per  sq.  in.  of  net 
section;  wood  in  tension.  800  to  900  lbs.  Wood  in  compression,  ^  to  i 
breaking  load,  by  S.  C.  Smith's  formula.  Wood  as  a  beam,  etc.,  800  to 
900  lbs.  per  sq.  in.  on  extreme  fibres  ;  keys,  post  blocks,  packing,  clamps, 
brace-blocks,  are  all  of  white  oak. 

The  147-ft.  spans  have  iron  clamps  and  lower  chord  post  blocks.  All 
spans  of  50  ft.  and  over  have  iron  brace  and  lateral  blocks,  except  the  50- 
ft.  through  span.  There  is  the  same  number  of  panels  of  lateral  bracing 
as  of  vertical  in  all  trusses.  Much  of  the  counter  bracing  is  in  excess.  In 
the  skeleton  diagrams  the  height  is  centre  to  centre  of  chords,  and  the 


HOWE  TRUSSES  ON  THE  CANADIAN  PACIFIC  RAILWAY.         145 

length,  from  face  to  face  of  end  post.  All  main  rods  have  upset  ends. 
Hexagonal  nuts  are  used,  with  8  to  10  ins.  of  thread  at  each  end.  With 
plates  no  washers  are  used.  The  lateral  rods  have  square  nuts  5  ina.  of 
threads,  all  upset. 

FORMULAS  FOR  WEIGHTS  OF  BRIDGES, 

The  following  formulas  for  computing  the  approximate  weights  of 
bridges  are  taken  from  Merriman's  Text  Book  on  Roofs  and  Bridges  : 

For  a  highway  bridge  let  I  be  the  span  in  feet,  6  the  width  in  feet  (in- 
cluding sidewalks,  if  any)  and  w  the  weight  in  pounds  per  linear  foot, 
then, 

w  =  UO  +  Vah  +  0.2  b  Z-  0.4  I. 

For  a  ray  road  bridge  the  weight  per  linear  foot  can  be  roughly  found 
from  the  following  formulas  for  spans  less  than  300  feet  in  length  : 

For  single  track  w  =  560  +  5.6  Z. 

For  double  tracks  =  1,070  -f  10.7  I. 

Wooden  bridges  weigh  about  the  same  as  iron  of  equal  strength. 


CHAPTER   YIII. 


Construction  Details. 

CENTRES  FOR  ARCHES. 

There  is  nothing  connected  with  the  construction  of  stone  or  brick 
arches  which  requires  more  careful  attention  on- the  part  of  the  builders 
than  the  centres — it  matters  not  what  the  shape  or  span,  or  for  what  par- 
ticular purpose  the  arch  be  intended.  Aside  from  the  choice  of  material 
and  the  care  with  which  other  parts  of  the  construction  are  performed, 
the  settlement  and  ultimate  stabiUty  of  the  arch  decidedly  depends  on  the 
framing,  setting  and  striking  of  the  centres.  The  yielding  of  a  brace  of 
improper  dimensions,  or  a  slight  change  in  the  shape  of  the  frame  caused 
by  an  iil-seasoned  timber,  may  result  in  so  changing  the  shape  of  the 
intrados  as  to  endanger  the  safety  of  the  arch.  It  must  be  the  object  of 
the  engineer,  in  all  largo-spanned  arches,  to  determine  by  what  combina- 
tion of  beams  and  by  what  system  of  bracing  the  greatest  strength  and 
stiffness  may  be  secured,  combined  with  lightness  and  economy  of 
materials. 

"When  in  position  the  centres  are  placed  about  5  to  7  feet  centre  to  cen- 
tre and  are  known  as  ribs.  Pieces  of  board  or  plank,  called  laggins,  are 
placed  horizontally  upon  them,  on  which  rest  the  voussoirs  until  the  key- 
stone is  inserted,  when  the  arch  becomes  self-supporting.  The  frame- 
work of  the  centre  consists  of  short  beams  which  are  cut  on  the  outer 
edge  to  form  parts  of  a  curve,  and  when  put  in  place  they  unite  to  form 
the  same  curve  as  the  intrados  of  the  arch.  These  are  held  in  place  by 
horizontal  tie-beams,  struts,  ties  and  braces,  the  arrangement,  number  and 
dimensions  of  which  will  depend  upon  the  shape  and  span  of  the  arch  as 
well  as  number  and  position  of  the  points  of  support. 

Experience  shows  that  whatever  be  the  shape  or  span,  the  arrange- 
ment of  the  ribs  in  the  form  of  a  polygon  is  the  best  in  every  case.  This 
shape  is  acquired  by  the  arrangement  of  the  short  beams  or  back-pieces, 
which  usually  consist  of  two  or  more  pieces  of  plank  firmly  nailed  to- 
gether and  abutting  end  to  end,  forming  a  joint  in  the  direction  of  the 
radius  of  curvature  of  the  arch.    It  is  obvious  that  the  strains  to  which 


CENTRES  FOR  ARCHES.  147 

the  centres  are  subjected  arise  slowly  from  the  pressure  upon  the  back- 
pieces  and  laggins.  Therefore  the  strains  depend  upon  the  span  and 
curve  of  the  arch  and  the  thickness  and  weight  of  the  voussoirs  which 
rest  upon  the  centring.  All  the  voussoirs  from  one  springing  line  to  the 
other  do  not.  however,  press  upon  the  frames.  This  depends  very  greatly 
upon  the  degree  of  curvature  of  the  arch.  In  a  full-centred  arch  the 
voussoirs  exert  no  pressure  upon  the  frames  for  a  considerable  distance 
above  each  springing  line,  but  when  the  point  is  reached  where  the  stones 
begin  to  exert  a  pressure  upon  the  frames,  such  pressure  increases  very 
rapidly  as  we  approach  the  crown  and  reaches  its  maximum  intensity 
just  before  the  key -stone  course  is  driven  into  place.  These  voussoirs 
which  lie  near  the  springing-plane  and  exert  no  pressure  upon  the  lag- 
gins  and  hack-pieces  are  all  situated  within  the  angle  of  repose — in  other 
words,  the  voussoirs  do  not  begin  to  press  upon  the  centring  until  we 
meet  one  whose  lower  joint  makes  so  great  an  angle  with  the  horizontal 
as  to  cause  it  to  slide  under  the  force  of  gravity. 

For  ordinary  cut  stone,  the  argle  of  repose  of  a  full-centred  arch  has 
been  found  by  experiment  to  be  about  30°;  but  if  the  stone  be  laid  in  full 
mortar  it  will  be  very  nearly  45°.  The  number  of  stones,  then,  that  will 
load  the  centre-frame,  taking  the  angle  of  repose  at  30°,  will  depend  en- 
tirely upon  the  form  of  the  curve  given  to  the  intrados.  For  example,  in 
a  full  centre,  an  oval  and  a  flat  segmental  arch ,  having  the  same  number 
of  Voussoirs,  it  is  plain  that  the  number  of  stones?  which  do  not  press  upon 
the  laggins  will  be  greatest  in  the  first-mentioned  arch,  less  in  the  second 
and  still  less  in  the  third.  Those  stones  which  do  press  upon  the  laggins 
do  not  do  so  with  their  entire  weight,  owing  to  the  friction  of  the  sur- 
faces of  contact  which  the  weight  of  the  stone  is  compelled  to  overcome. 

According  to  Rankin  e  the  total  weight  of  each  stone  which  presses 
upon  the  laggins  is  to  the  weight  with  which  they  actually  load  the  frame 
as  an  arc  of  60'  is  to  twice  its  sine  lass  the  same  angle,  or  the  relation  may 
be  thus  expressed  : 

Let  W  =  total  weight  of  voussoirs  which  rest  on  centring 

and  w  —  weight  with  which  they  load  centring. 

Then  we  have  W  '.w  :  :  arc  60°  :  2  sin  60°  —  arc  60°, 

W  (2  sin  60°  —  arc  60°). 

or  w  = ' 

arc  66 

Now  let  the  radius  be  divided  into  any  number  of  equal  parts,  say  r  = 

15000.     The  circumff^rence  will  then  contain  94248  and  the  arc  of  60   — 

15708.    The  sine  of  the  arc  of  60°  will  be  r  X  i  Vg  =  r  X  .8660  =  12990. 


148  CONSTRUCTION  DETAILS. 

Substituting  these  values  in  the  above  equation  we  have 

W:w::  15708  :  2  X  12990  —  15708, 
which  gives  a  ratio  of  3  to  2,  nearly. 

We  therefore  conclude  that  about  |  of  the  weight  of  those  stones  which 
lie  without  the  angle  of  repose  actually  press  upon  the  laggins  :  and  tak- 
ing into  account  the  60''  contained  in  the  angles  of  repose  on  both  sides, 
we  find  that  about  f  X  |  =  f  of  the  gross  weight  of  the  arch  expresses 
the  load  of  the  centres.  The  case  is  entirely  similar  with  arches  which 
are  not  full  centred.  In  order,  then,  to  determine  the  gross  weight  of 
that  portion  of  the  arch  which  presses  on  the  back  pieces  and  laggins  and 
causes  stresses  in  the  framework  of  the  centres,  it  is  only  necessary  to 
know  the  number  of  voussoirs,  their  volume  and  weight  per  cubic  foot. 
If  the  centres  are  subject  to  other  stresses  besides  those  caused  by  the 
voussoirs,  as  is  sometimes  the  case  in  tunneling  where  the  timbering  is 
removed  before  the  keystone  course  is  driven,  such  additional  stresses 
must  be  provided  for. 

The  direction  and  intensity  of  strains  caused  by  the  voussoirs  may 
easily  be  found  by  resorting  to  parallelogram  of  forces. 

For  example,  the  weight  of  any  arch  stone  or  any  number  of  arch  stones, 
which  acts  vertically  downward  through  its  centre  of  gravity,  may  be 
resolved  into  two  components,  one  of  which  will  be  normal  to  the  lower 
radial  joint  of  the  arch  and  will  represent  in  magnitude  and  direction  the 
weight  which  is  not  supported  by  the  rib,  but  which  is  resisted  by  the 
lower  part  of  the  arch  and  finally  by  the  abutment,  and  the  other  in  the 
direction  of  tne  radius  of  curvature  of  the  intrados  representing  in  mag- 
nitude and  direction  the  weight  which  must  be  resisted  by  the  centring. 

The  strains  then  take  the  direction  of  the  radius  of  curvatiire  of  the  in- 
trados. Now,  to  find  the  position  of  the  beams  which  are  to  withstand 
these  strains,  also  their  number  and  dimensions,  is  next  required.  It  is 
evide.it  that  a  horizontal  beam  loaded  at  its  middle  will  offer  its  least  re- 
sistance to  the  load.  If ,  now,  one  end  of  the  beam  be  raised  so  that  the 
direction  of  sti'ain  is  oblique  to  the  fibers  of  the  beam,  the  resistance  in  the 
latter  case  will  be  to  that  in  the  former  as  the  cosine  of  the  angle  made  by 
the  direction  of  the  strain  and  the  fibres  of  wood  is  to  sine  90 "^  or  1.  It 
should  follow  that  when  the  angle  between  the  beam  and  strain  is  zero 
the  resistance  becomes  infinite,  and  if  it  were  not  for  the  compressibility 
and  certain  other  physical  causes  such  would  be  the  case.  However  this 
may  be,  the  beam  is  certain  to  be  strongest  in  the  direction  of  its  fibres, 
hence  the  greatest  stiffness  and  strength  will  be  gained  when  the  principal 


CENTRES  FO.   ARCHES.  149 

pieces  are  placed  in  the  direction  of  the  strains;  that  is,  in  the  direction 
of  the  radius  of  curvature  of  the  arcli.  The  practical  application  of  this 
arrangement  of  beams  is,  however,  r'^stricted  t )  small  arches,  because 
when  timbers  are  30  or  40  feet  long  it  fails  utterly.  For  while  a  beam  of 
10  feet  long  will  offer  great  resistance  to  compression  in  the  direction  of 
its  fibers,  a  beam  40  feet  long  w^ould  be  sure  to  bend  and  require  bracing. 
In  order,  therefore,  to  arrive  at  an  arrangement  which  will  adapt  itself  to 
large  arches,  if  we  resolve  the  radial  stresses  of  two  symmetrical  portic  ns  of 
the  arch,  with  respect  to  a  vertical  plane  through  the  center  of  the 
arch  and  in  the  direction  of  its  length,  into  horizontal  and  vertical  com- 
ponents, these  components  will  represent  the  direction  of  three  beams,  one 
horizontal  spanning  the  arch  and  supported  at  each  end  by  a  vertical 
beam.  According  to  Drinker  on  Tunneling,  this  horizontal  beam  is  placed 
about  45"  up  the  arch,  in  practice.  The  voussoirs  above  this  tie  beam  are 
then  supported  by  another  horizontal  tie  beam  upheld  by  small  vertical 
beams  abutting  on  the  lower  tie. 

Now,  then,  knowing  the  pressure  exerted  on  the  centre,  and  being  able 
to  calculate  the  pressure  upon  any  segment  thereof  ;  also,  having  decided 
upon  the  number  and  arrangement  of  members,  the  strains  may  be  found 
either  analytically  or  by  the  graphical  method.  After  determining  the 
stresses  the  members  may  be  proportioned  vpith  Gordon's  formula,  using 
a  factor  of  safety  of  4  to  6. 

The  centring  should  be  slightly  higher  in  the  middle  than  the  intended 
height  of  the  finished  arch,  in  order  to  allow  for  deflection.  By  experi- 
ence the  amount  of  deflection  is  found  to  be  ^^^  of  the  radius  of  curvature. 
The  centring  must,  therefore,  be  made  ^^  of  r  higher  at  the  crown  than 
the  finished  arch  is  intended.  When  the  keystone  course  has  been  driven 
the  striking  of  the  centres  must  be  deferred  for  some  days,  or  even  weeks, 
in  order  to  give  the  cement  time  to  settle  properly.  It  has  been  found  by 
experience,  however,  that  it  is  well  to  very  slightly  withdraw  the  cen- 
tring soon  after  the  arch  is  finished,  in  order  to  allow  for  the  deflection  be- 
fore the  cement  is  perfectly  settled.  A  very  satisfactory  method,  with 
this  object  in  view,  is  to  have  the  centring  supported  by  means  of  hol- 
low cylindrical  columns  filled  with  sand.  The  weight  rests  on  the  sand 
by  means  of  pistons,  which  project  into  the  top  of  the  column,  while  the 
pillars  rest  on  solid  foundations.  There  is  a  small  opening  near  the  bottom 
of  each  pillar,  and  when  the  arch  is  ready  to  be  decentred  a  small  por- 
tion of  the  sand  is  let  out,  thus  allowing  the  arch  to  deflect  very  gradu- 
ally. N.  J.  Wither. 


150 


CONSTRUCTION  DETAILS. 


REPAIRS  TO  THE  ARCH  OF  THE  MUSCONETCONG  TUNNEL. 


[Published  by  permission  of  the  Lehigh  Valley  Railroad  Co.] 

The  Musconetcong  Tunnel  is  situated  in  New  Jersey,  on  the  ]ine  of  the 
Lehigh  Valley  Railroad,  about  twelve  miles  from  Easton.  lu  the  autumn 
of  1871  and  the  winter  of  1873  the  location  was  decided  upon.  The  road 
was  at  that  time  divided  into  four  divisions,  Mr.  Robert  H.  Sayre,  Chief 

Engineer  of  the  Lehigh  Valley  Rail- 
road, being  also  Chief  Engineer  of 
the  Easton  &  Amboy  Division,  in 
which  the  tunnel  is  located.  Mr.  Cal- 
vin E.  Brodhead  was  Principal  Assist- 
ant ;  Mr.  John  L.  Wilson,  Division 
Engineer ;  Mr.  Henry  S.  Drinker, 
Resident  Engineer,  and  Mr,  Charles 
McFadden,  of  Philadelphia,  Con- 
tractor. 

The  tunnel  is  through  a  spur  of 
the  Musconetcong  Mountains  (that 
range  which  extends  over  Northern 
New  Jprsey  and  into  Southern  New 
York),  and  is  5,136  feet  long.  At  the 
west  end  it  passes  through  770  feet 
of  soft  ground,  702  feet  of  which  is 
arched,  the  remainder  being  taken 
out  in  open  cut,  450  feet  of  lime- 
stone, 263  feet  of  loose  rock  and 
3,731  feet  of  syenite,  declared  by 
competent  judges  to  be  harder  and 
tougher  than  any  rock  encountered 
along  the  line  of  the  Hoosac  Tunnel. 
In  April.  1872,  ground  was  broken  on  the  west  cut.  work  starting  soon 
after  on  the  east  end,  and  in  December,  1874,  the  headings  met.  It  was 
decided  to  commence  by  a  slope  down  to  the  level  of  the  proposed  head- 
ings, which  were  then  to  be  run  in  both  directions.  This  was  on  the  west 
end  in  the  earthy  portion  of  the  tunnel,  the  east  end  being  run  full  size. 
Tiie  slope  having  been  dug,  work  was  commenced  on  the  headings,  but 
the  ground  was  very  heavy,  requiring  careful  timbering.      Springs  of 


REP AI RS  TO  A  RCH  OF  MUSCONETCONG  TUNNEL.  15 1 

water  were  constantly  encountered,  and  finally  one  spring  struck  with 
which  two  large  pumps  were  unable  to  cope  ;  the  water  gained  rapidly, 
the  timbering  was  undermined  and  the  entire  work  ruined.  After  this 
the  slope  was  abandoned  ;  a  shaft  was  sunk  to  the  west  and  headings  run 
each  way  until  the  water  was  struck,  when  it  was  carried  out  through 
the  west  heading.  This  portion  of  the  tunnel  was  the  most  troublesome, 
and  has  kept  up  its  reputation  in  this  respect  ever  since. 

That  portion  of  the  tunnel  throi'.gh  the  earth,  and  also  where  the  loose 
rofk  was  encountered  at  the  junction  of  the  limestone  and  the  syenite, 
was  arched,  there  being  50  feet  of  stone  arching  at  the  west  end,  the  re- 
mainder of  brick.     The  backing  was  dry  rubble. 

For  a  number  of  years  the  brick  arch  gave  good  satisfaction,  but  finally 
it  began  to  fail.  Longitudinal  cracks  were  opened,  and  at  last  it  grew  so 
bad  that  the  bricks  would  fall  out  under  the  jarring  of  the  passing  trains. 
The  cause  of  this  failure  is  not  known,  the  mortar  used  not  having  been 
injured  by  the  water,  as  afterwards  proved.  It  is  probable  that  the 
rubble  backing  was  not  packed  tight  enough,  thus  allowing  a  pressure 
from  above  to  be  transmitted  directly  to  that  portion  of  the  arch  below, 
instead  of  being  distributed  uniformly  over  the  entire  arch. 

Several  remedies  were  suggested  and  plans  made,  but  first  it  became 
necessary  to  timber  the  failing  part,  or  there  was  danger  of  the  entire  arch 
collapsing.  The  great  problem  was  to  put  in  solid  timbering  and  still  not 
interfere  with  the  trains.  The  double  track  was  changed  to  a  single  one 
raised  on  sills  and  timbering  put  in  as  showi  in  Figs.  1  and  2.  The  first 
kind  (Fig.  1).  was  used  for  255  feet  at  the  west  end,  215  feet  of  this  having 
knees,  and  410  feet  of  the  second  kind  (Fig.  2).  The  tunnel  starts  at 
station  676+65,  and  at  station  678  +  20  double  timbering  was  used  on 
account  of  the  character  of  the  arch  at  that  point.  The  bents  are  five 
feet  apart,  centre  to  centre,  of  pine  and  hemlock,  the  sills  are  8"  X  12", 
the  posts  12"  X  12",  and  the  corbels  12"  X  12".  To  withstand  any  lateral 
pressure  the  bents  are  connected  by  short  struts,  12"  X  12"  hemlock.  It 
will  be  seen  by  an  inspection  of  the  figures  that  this  timbering  is  put  up 
in  the  most  substantial  manner.  The  second  kind  is  considered  the  best, 
as  in  it  no  distortion  can  take  place  unless  the  bents  break.  This  work 
was  commenced  in  April,  1888. 

As  for  repairing  the  arch,  many  plans  were  suggested.  One  was  to  take 
out  the  old  arch  in  sections  and  replace  it  by  a  stone  arch ;  another,  to  take 
out  the  old  arch  as  above,  replacing  it  by  a  concrete  one  resting  upon  the 
old  side  walls.     Neither  of  these  was  adopted,  but  after  much  dellhera- 


153  CONSTRUCTION  DETAILS. 

tion  it  was  decided  to  excavate  above  the  old  arch  and  back  of  the  old 
walls  and  fill  in  with  concrete,  removing  the  old  arch  after  the  concrete 
had  set. 

In  June,  1888,  the  old  shaft  was  opened,  and  a  heading  run  both  ways 
along  the  crown  of  the  arch.  This  heading  was  6  feet  by  6  feet,  through 
very  heavy  earth  and  heavy  timbering  :  bull  pine  in  pieces  of  from  10  to 
12  inches  diameter  was  used  and  proved  very  satisfactory;  it  was  much 
more  economical  than  hemlock,  costing  less  than  one  third  as  much  per 
running  foot.  The  bents  were  put  3  feet  apart,  centre  to  centre,  allowing 
a  clear  space  of  5  feet  by  5  feet.  Above  Fig.  2  is  shown  the  method  of 
timbering  these  headings.  After  being  run  for  about  fifty  feet  the  head- 
ing was  then  extended  down  along  the  line  of  the  arch  to  a  firm  founda- 
tion back  of  the  side  walls,  every  other  bent  being  knocked  out 
for  this  purpose  and  replaced  by  timbering  as  shown  in  Fig.  1.  Along  the 
crown  of  the  arch  6-inch  scantling  were  laid  on  which  the  sills,  6  inches  by 
12  inches  rested  to  support  the  stubs.  Concrete  was  then  put  into  a  thick- 
ness of  from  4  to  4|  feet  on  the  walls  and  haunches  to  3  feet  6  inches  on 
the  crown,  thoroughly  tamped,  and  the  space  above,  about  3  feet,  tightly 
packed  with  dry  rubble,  the  stories  being  about  1  i  feet  each  way.  The 
concrete  was  mixed  in  the  following  proportions,  by  bulk  : 

A  Isen's  German  Portland  eement  I 

Clean  sand 254 

Stone 6^ 

The  sand  was  from  Perth  Amboy  and  of  a  high  order,  consisting  al- 
most entirely  of  quartz  with  little  or  no  loam  ;  the  stone  was  that  taken 
from  the  old  tunnel,  syenitic  gneiss  and  limestone.  The  concrete  set 
thoroughly  in  four  hours. 

It  was  found  expedient  after  the  work  had  progressed  to  open  a  new 
shaft.  The  old  one  was  140  feet  deep,  and  330  feet  west,  or  150  ft.  from  the 
end,  of  the  tunnel  was  sunk  the  new  one.  From  this  shaft  the  headings 
were  run  to  the  ring  stones  of  the  tunnel  facing.  The  old  shaft  was  filled 
with  5  feet  of  concrete,  14  feet  of  puddled  clay,  and  the  remainder  with  the 
material  from  the  tunnel.  A  Copeland  &  Bacon  (N.  Y.)  hoisting  drum 
was  iised. 

The  concrete  invert  was  put  in  in  30-f  t.  sections  on  Sundays,  The  wedges 
above  the  corbels  being  driven  out,  the  beats  were  jacked  up  and  after- 
wards put  down  on  6"  X  12"  blocks.  The  invert  was  laid  to  the  arc  of  a 
circle  of  44  feet  radius,  21  inches  thick  at  the  extremities,  15  inches  at  the 


STANDARD  FENCES  AND  GATES.  158 

middle,  laid  to  a  form.  It  was  kept  clear  of  water  while  this  work  was 
going  on  by  a  Worthington  (N.  Y.  and  London)  pump  ;  at  the  same  time 
by  levers  this  water  could  be  thrown  up  the  hill  through  a  1^  inch  pipe  to 
be  used  in  mixing  the  concrete.  This  mixing  was  all  done  near  the 
shafts,  the  concrete  being  taken  down  for  use  in  the  invert  on  an  inclined 
railway,  a  car  descending  pulled  up  an  empty  one.  For  pumping  the 
water  from  the  backing  a  Blake  (N.  Y.  and  Boston)  pump  was  used.  Fig. 
3  shows  the  lines  of  the  concrete  arch. 

While  removing  the  arch,  the  back  of  the  masonry  was  so  foul  that  an 
air  drum  had  to  be  put  in.  This  was  a  Sturtevant  (Boston)  drum  which 
is  guaranteed  to  deliver  10,000  cubic  feet  of  air  per  minute,  runnins  600 
revolutions.  The  air  was  carried  along  by  a  wooden  box  11 1  by  36  inches 
interior  dimensions  through  the  tunnel,  and  back  of  the  masonry  by 
branch  boxes  10  inches  by  12  inches  interior.  With  a  pressure  of  85 
pounds  in  the  boiler  this  drum  made  560  revolutions.  Before  it  was  put 
in,  a  number  of  men  had  been  prostrated  while  workiug  behind  the  arch. 

After  the  concrete  had  been  in  thirty  days,  the  brick  arch  and  sidewalls 
were  taken  out;  the  50  feet  of  stone  arching  being  in  excellent  condition 
was  not  touched.  The  result  is  a  tunnel  with  many  unique  features,  and 
engineers  may  well  be  impatient  to  learn  how  the  concrete  arch  will 
hold. 

Thanks  are  due  to  the  officers  of  the  Lehigh  Valley  Railroad  for  their 
courtesy  to  the  writer  in  giving  him  free  access  to  the  tunnel  and  to  the 
plans.  Thos.  C.  J.  Baily,  Jr. 


STANDARD  FENCES  AND  GATES. 

On  so  long  a  line  as  the  Canadian  Pacific  Railway  there  are  all  kinds  of 
fences,  according  to  local  conditions,  and  on  a  very  large  part  of  the  way 
no  fence  at  all;  but  the  standard  fence  and* gate,  which  has  been  more 
used  than  any  other,  is  that  of  a  four-wire  fence  with  a  board  cap 
and  top  board.  The  two  alternate  constructions  for  rock  has  been  quite 
frequently  necessary,  there  being  considerable  distances  where  fence  is 
required,  but  where  there  is  not  soil  enough  to  make  it  convenient  to  sink 
fence  posts.  The  gate  is  a  solid  and  good  one,  and  proves  quite  satisfac- 
tory when  properly  put  up.  All  depends,  <5f  course  on  having  the  posts 
well  set  in  the  ground. 


lo4  CONSTRUCTION  DETAILS. 


UNDERSTRUCTURE   FOR   A  40,000-GALLON   TANK,    CANADIAN 
PACIFIC   RAILWAY. 

In  the  tank  the  elevation  of  bottom  of  sills  is  2  ins.  above  base  of  rail. 
The  air  chamber  joists  are  4x8  ins,,  the  upper  and  floor  joists  3  X  12 
ins.  ;  the  sheeting  and  girting  2x4  ins.  ,  the  braces  and  the  struts  4x6 
ins. ,  and  the  diagonal  sills  4  X  12  ins.  All  the  rest  of  the  timber  except 
the  9  X  9  in.  diagonal  cap  is  13  X  12  ins.  The  sheeting,  inside  and  out- 
side, is  i  in.,  dressed,  seasoned  and  tongued  and  grooved.  The  tie  rods  are 
1  in.,  with  nuts  at  each  end,  and  1  in.  square  drift  bolts,  24  ins.  long,  are 
used  for  connections.— P.  C.  Girouard,  in  Engineering  Netcs. 


PILE  DRIVING  MACHINE. 


155 


PILE   DRIVING    MACHINE. 
The  machine  illustrated  is  one  of  the  very  latest  in  model,  and  the 
heaviest  in  New  York  harbor, 

Fi^.  6 .  /lanimer' 
-T 


Cross ySec.-lon^. bulkheacla  


Details  of  Pile  Driving  Machine. 


156  CONSTRUCTION  DETAILS. 

The  hull  is  56  ft.  6  ins.  long  and  23  ft.  6  ins.  wide  over  all;  each  of  the 
sides  of  the  hull  is  made  of  four  pieces  of  yellow  pine,  the  two  lower  each 
8  X  14  in.,  the  third  7  X  14  in.,  the  top  piece  6  X  14  in.,  all  securely  tied 
by  through  bolts;  the  bow  planking  is  oak,  5  ins.  thick;  the  bottom  and 
end  plank  yellow  pine,  3  ins.  thick.  The  bow  is  further  strengthened  by 
a  16  X  16  in.  cross  timber  at  top,  and  at  the  stern  is  an  8  X  12-in.  cross 
timber  of  yellow  pine.  Oak  is  used  on  the  bow  as  being  better  adapted 
to  stand  the  constant  wear  of  the  piles  hauled  against  it,  and  to  prevent 
knots  or  inequalities  on  the  piles  interfering  with  their  position  under  the 
hammer;  the  bow  planking  overhangs  6  ins.  in  its  total  height. 

The  chief  end  in  the  design  of  a  hull  for  a  floating  pile  driver  is  to 
obtain  longitudinal  stiffness,  so  that  the  strains  between  the  bow  and 
engine  may  be  properly  distributed.  To  this  end  our  hull  is  strengthened 
lengthwise  by  four  wooden  bulkheads  or  kelsons,  each  6  ins.  thick  (Fig.  2) 
and  braced  laterally  by  four  sets  of  X  braces  of  6  x  6  timber.  The  hull 
is  further  braced  in  the  center  by  two  3  X  13  in.  Y.  P.  braces,  and  tie  rods 
or  "hog  chains"  of  iron,  If  ins.  in  diameter.  Wale  pieces  and  fender 
plank  3  ins.  thick  protect  the  outside  of  the  hiill  against  chafing;  the  deck 
has  a  "crown"  of  about  6  ins.  in  its  total  width. 

The  hammer-guides  are  made  of  two  pieces  of  12x12  Y.  P.  67  feet 
long  from  out  to  out  with  inside  guides  of  5x4  in.  stuff  protected  by 
plate  iron  i  ins.  thick ;  f-in.  bolts  with  countersunk  heads  fasten  the 
inner  guides  to  the  main  sticks  and  at  the  same  time  secure  the  iron  work 
to  the  same.  The  bottoms  of  the  main  guides  are  connected  with  the 
12x13  bed  pieces,  shown  in  Fig.  3,  by  two  timber  knees,  and  are  tied  at 
top  by  the  cap  shown  in  Fig.  6. 

The  dimensions  and  general  arrangement  of  the  back-bracing  is  fully 
shown  in  Figs.  1  and  3  ;  the  bolts  used  in  this  portion  of  the  frame  work 
are  |  in.  diameter.  The  side  braces  are  round  timbers  16-ins.  diameter 
at  the  butt,  and  they  are  anchored  to  the  hull  by  two  heavy  timber 
knees  to  each.  The  bed  pieces,  as  shown  at  Fig.  3,  are  fastened  down  to 
the  hull  by  four  bolts  each,  1  in.  in  diameter,  the  forward  bolts  passing 
through  the  16xl6-in.  oak  piece  on  bow,  and  the  after-bolts  passing 
into  a  cross  timber  6x  14  ins. ,  as  shown  at  Fig.  4.  The  foot  of  the  back- 
bracing  is  secured  to  the  bed  timbers  by  one  1  in.  strap-bolt  in  each 
timber,  the  strap  portion  of  bolt  being  2xi  in.  in  section.  A  -J-in. 
through-bolt  ties  the  three  braces  together. 

The  iron  stay-rods  running  from  head  of  guides  to  after  part  of  hull 
are  two  in  number,  and  are  each  1  in.  in  diameter. 


PILE  DRIVING  MACHINE. 


157 

•*  e 


LonjlSec.  showing'  internal  bracing-  


158  CONSTRUCTION  DETAILS. 

The  hoisting  shaves  on  top  are  two  in  number,  placed  side  by  side. 
They  are  12  ins.  in  working  diameter,  1^  ins.  from  out  to  out,  and 
Si  ins.  wide ;  and  the  pin  passing  through  them  is  2|  ins.  diameter 
at  the  sheaves,  and  2  ins.  diameter  in  the  boxes.  Experience  teaches 
that  these  proportions  are  none  too  great  to  stand  the  severe 
work  frequently  put  upon  it  in  hoisting  heavy  weights  and 
tearing  out  timber.  The  fall  rope  attached  to  the  hammer  is  2  ins.  in 
diameter,  and  the  "  runner"  used  in  hoisting  up  piles  is  If  ins.  diameter. 

The  hoisting  engine  is  a  double-drummed  Mundy  engine  of  a  nominal  25 
horse  power. 

Fig.  5  shows  the  hammer  used  with  this  machine.  The  drawing  is 
suflBcient  to  show  its  general  design.    The  weight  is  3,300  jhs. 

Fig.  7  shows  the  method  of  attaching  the  two  5  X  12  in.  horizontal 
braces  to  the  round  side  braces,  as  further  shown  in  Fig.  2. 


THE  AGE  OF  RAILROADS  IN  DIFFERENT  COUNTRIES. 

England September  27,  1825 

Austria September  30,  18::^ 8 

France October  1,  1828 

fhe  United  States December  28,  1829 

Belgium May  3,  1835 

Germany     December  7,  1835 

Island  of  Cuba In  the  year  1837 

Russia •. April  4,  1838 

Italy September,  1839 

Switzerland July  15,  1844 

Jamaica November  21,  1845 

Spain October  2t,  1848 

Canada May,  1850 

Mexico In  the  year  1850 

Sweden  and  Peru In  the  year  1851 

Chili   January,  1852 

East  Indies ..       April  18,  1853 

Norway July,  1853 

Portugal  In  the  year  1854 

Brazil   April  30,  1854 

Victoria September  14,  1854 

Colombia .   January  28,  1855 

New  South  Wales September  25,  1855 

Egrypt  January,  1856 

Middle  Australia April  21, 1856 

Natal June  26,  1860 

Turkey October  4,  i860 


RULES  FOR  MEA.SURING  WORK-MAKINCJ  DRAWINGS.  159 


RULES  FOR  MEASURING  WORK. 

Measure  stone  work  by  the  cubic  foot,  plastering  by  the  square  yard, 
brick  work  by  the  cubic  foot  (30^  brick  to  the  cubic  foot) ;  roofingr,  ol 
slate,  tin,  gravel  or  shingles,  by  the  square  of  100  feet — thus,  10  X  10  = 
100  square  feet ;  flooring  the  same  ;  roof -painting  by  the  square,  same  as 
flooring  ;  for  house  painting  there  is  no  rule.  These  are  the  rules  geuer- 
aily  followed  in  New  York,  and  their  universal  use  would  be  advantage- 
ous. 


DIRECTIONS  FOR  MAKING  DRAWINGS  FOR  REPRODUCTION. 

1 .  Use  a  paper  with  a  smooth  surface  rather  than  a  Whatman  or  othe? 
paper  with  a  rough  surface.  What  is  called  "  ledger"  paper,  smooth, 
heavy  and  white,  is  well  adapted  to  this  purpose. 

2.  Use  very  black  India  ink  ;  the  prepared  liquid  India  ink  is  very  good 
and  is  always  ready. 

3.  Have  your  drawing-pen  in  good  condition,  so  that  the  lines  are  sharp 
and  well  defined. 

4.  Use  as  few  shade  lines  as  possible;  or  if  used  let  them  be  sharp  and 
well  defined,  not  too  close  together,  and  in  cylindrical  work  decreasing  in 
thickness  of  line  as  the  light  is  approached. 

5.  Make  the  original  drawing  at  least  four  times  the  size  of  the  electro- 
plate wanted.  The  work  is  much  improved  in  appearance  by  being  thus 
reduced,  as  the  lines  are  finer,  and  slight  errors  in  drawing  are,  to  a  cer- 
tain extent,  decreased  in  importance. 

6.  In  this  reduction  remember  that  all  lettering  and  figures  will  be  re- 
duced in  proportion.  Consequently  in  the  drawing  this  lettering  and 
figure  work  should  be,  say,  twice  as  high  as  thpy  are  intended  to  appear 
on  the  finished  plate,  in  a  drawing  to  be  reduced  to  one-fourth. 

7.  Draw  the  scale  on  the  original  so  that  it  may  be  reduced  with  it. 
Unless  the  reproduced  plate  is  to  be  of  exactly  the  same  size,  the  mere 
mention  of  the  scale  has  no  value. 

8.  Avoid  all  brush  shading  and  color  other  than  dense  black. 


160 


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intellectually  and  oractically  than  he  cannot  at  times  add  to  his  knowledge  fro-" 
the  paores  of  Enginkkring  News;  to  the  young  engineer  just  Htruggling  "for  place" 
in  hi^  profession,  there  can  be  no  agency  more  helpJhil  than  the  weekly  installment 
of  this  journal. 

The  \^th  year  and  29th  volume  of  Engineering  News  will  commence  on  Jan. 
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APPENDIX. 


BOOKS  KOR  RAIIvROAD   KNGINEERS. 

The  studies  of  a  young  raili'oad  engineer,  who  has  not  had  the 
advantages  of  a  technical  education,  naturally  lie  in  the  same  direc- 
tion as  those  piu'sued  by  students  in  engineering  schools.  In  general,  it 
may  be  said  that  a  list  of  books  used  in  such  schools  would  be  au  ad- 
\antageous  one  for  the  young  railroad  engineer  to  follow,  but  such 
lists  can  be  obtained  by  applying  for  catalogues  of  the  institutions 
themselves.  We  will  not,  therefore,  hen.  attempt  to  give  an  outline 
of  such  formal  courses  of  study,  although  some  of  the  books  will  be 
mentioned  under  the  separate  headings  below. 

MATHEjMATiCS.  • 
There  are  so  many  excellent  series  of  mathematical  text-books,  that 
a  selection  of  any  single  one  would  be  a  difficult  matter,  and  might 
almost  seem  invidious.  The  works  of  Simon  Newcomb,  professor 
in  the  United  States  Naval  Observatoiy  and  in  Johns  Hopkins  Uni- 
versity, are  extensively^  used  in  the  technical  schools,  and  take  a 
desen-edly  high  rank.  Among  others  may  be  mentioned  the  books  of 
Professor  Bowser,  of  Rutgei-s  College,  and  those  of  the  late  Professor 
Olney,  of  the  University  of  Michigan.  It  should  be  said  that  in  these 
and  many  other  series  there  are  elementaiy,  collegiate  and  also  ad- 
vanced works.  It  would  probably  be  best  for  the  railroad  engineer 
to  purchase  an  advanced  algebra  or  calculus,  rather  than  an  elementary 
or  an  intenuediate  one;  for  the  first  certainly  contains  all  that  the 
others  do,  and  besides  has  the  advantage  of  covering  the  ground  in 
a  manner  more  complete,  so  that  it  may  sers^c  for  a  reference  book. 
In  higher  mathematics,  the  field  engineer  will  rarely  have  the  time  or 
opportunity  to  read  many  works,  but  Muir's  Detenninants,  Hardy's 
QuatoiTiions  and  Baker's  EUiptic  Functions  may  be  noted  as  books 
introducing  to  the  higher  analysis.  Ball's  Short  Account  of  the  His- 
toi*y  of  M:itlu<matics  (12mo,  464  pages),  is  an  interesting  work  for  all 
with  mathematical  tendencies.     The  thorough  treatise  of  Carll  on  Cal- 


163  APPENDIX. 

cuius  of  Variations  (8vo,  $5),  has  special  interest  from  the  fact  that 
its  author  is  blind.  The  best  mathematical  cyclopedia  is  Carr's 
Synopsis  of  llesults  in  Pm-e  Mathematics  (London,  1S8G,  large  8vo,  035 
pages,  $13.50). 

SURVEYING. 
The  standard  works  on  railroad  surveying  are  generaly  known  to  the 
young  raih-oad  engineer.  Among  these  Searles'  Field  Engineering 
(fifteenth  edition,  pocket  foim,  $3),  is  usually  considered  to  be  one  of 
the  best,  both  in  theoretical  and  practical  lines,  and  its  tables  are 
certainly  most  excellent  for  ready  use  in  the  held.  The  held  book 
of  Shunk,  and  that  of  Henck,  have  also  been  extensively  used,  and 
Searles  has  a  separate  small  work  on  The  Railroad  Spiral.  In  the 
sm'vej'  of  public  lands,  the  best  work  is  the  Manual  of  Surveying,  by 
F.  Hodgman  (tifth  edition,  with  tables,  $2.50).  As  a  general  work, 
however,  Johnson's  Theory  and  Practice  of  Surveying  (ninth  edititju, 
754  pages,  150  cuts,  with  folding  maps  and  tables,  $4)  may  be  said 
to  cover  in  an  excellent  manner  the  subjects  of  land,  city,  topographic 
and  geodetic  survejing.  Special  books  on  the  last  mentioned  branch 
will  be  noted  below  under  Astronomy. 

•  TABLES. 

The  best  six-place  logarithmic  tables  with  which  we  are  acquainted 
are  those  in  Searles'  Field  Engineeilng,  mentioned  above.  It  is,  how- 
ever, a  matter  of  regi'et  that  five-place  tables  have  not  been  given 
in  field  books,  since  they  are  far  more  convenient  and  are  sufficiently 
accurate  for  problems  in  railroad  surveying.  Ludlow's  Tables  (8vo, 
$2),  is  an  excellent  set  of  five-place  logarithms  for  office  use,  which 
compare  favorably  with  the  Gei-man  ones  of  Gauss  and  Schoen. 
Among  seven-place  tables  those  of  Vega  and  Schroen  are  coiuited 
among  the  best,  the  former  having  old  style  type  and  the  latter 
modem  type.  In  geodetic  work  eight-place  logarithms  are  sometimes 
needed,  and  for  this  purpose  Vega's  Tliesaunis  Logarithmomm,  giving 
ten-place  tables  shoidd  be  used;  a  photolithogi-aphic  reproduction  of 
this,  with  all  errors  corrected,  has  lately  been  published  at  a  low 
price. 

MECHANICS. 

The  subject  of  mechanics  includes  the  fundamental  principles  which 
underlie  all  field  construction,  and  particularly  the  design  of  arches, 
bridges,  trestles  and  machinery.  It  is  properly  regarded  as  one  of  the 
most  important  studies  in  enghieering  schools.      Wood's  Principles  of 


APPENDIX.  168 

Elementary  Mechanics  (now  iu  its  ninth  edition,  12mo,  $1.25)  is  a 
standard  book,  whicli  sets  forth  the  fundamental  principles  in  a 
clear  and  simple  manner.  An  advanced  work  by  the  same  author 
is  the  Elements  of  Analytical  Mechanics  (seventh  edition,  about  500 
pages,  octavo,  $3),  and  there  are  also  many  excellent  books  by  other 
American  authors.  Meriiman's  Mechanics  of  Materials  (fourth  edition, 
octavo,  iuterleaved,  $3.50)  treats  of  the  strength  of  materials  and  the 
theory  of  beams,  colmnns  and  shafts.  Among  other  works  Lanza's 
Applied  Jlechanics  (fifth  edition,  929  pages,  $7.50)  and  Church's  Me- 
chanics of  Engiueering  (834  pages,  octavo,  $6),  may  be  noted  as  well 
known,  both  in  technical  schools  and  as  books  of  reference  by  en- 
gineei*s.  The  special  practical  applications  of  mechanics  are  found 
in  books  noted  below  under  the  headings  of  Roofs  and  Bridges,  Con- 
struction and  Hydrauhcs. 

ARCHITECTURE. 
Kidder's  Architects'  and  Buildei-s'  Pocket-Book  (tenth  edition,  883 
pages,  with  over  400  illustrations)  is  a  standard  work  iu  the  archi- 
tectural profession,  occupying  indeed  the  same  place  that  Trautwine's 
does  to  the  Civil  Engineer.  Birkmire's  Architectural  Iron  and  Steel 
(second  edition,  201  pages,  $3.50),  gives  the  most  recent  details  con- 
cerning the  use  of  iron  and  steel  in  architectural  engineering.  Mer- 
rill's Stones  for  Building  and  Decoration  (a  i-ecent  work,  octavo,  453 
pages,  $5)  gives  an  excellent  general  outline  of  the  physical  and 
chemical  properties  of  building  stones,  together  with  a  description  of 
quaiTy  methods,  stone  working  machines  and  the  weathering  and 
preservation  of  building  stones.  Berg's  Buildings  and  Stnictures  for 
American  Railroads  (quarto,  5(X)  pages,  691  figures,  $7.50)  is  an  exhaus- 
tive practical  work  which  eveiy  division  or  resident  engineer  shoxdd 
have  on  his  desk. 

ASTRONOMY  AND  GEODESY. 
Few  astronomical  problems  are  required  in  the  practice  of  a  rail- 
road engineer.  The  introduction  of  electric  railways,  however,  which 
are  often  to  be  built  in  straight  lines  between  distant  points,  requires 
the  detemiination  of  azimuth.  The  elementary  methods  for  this 
purpose  are  given  in  books  of  surveying,  but  when  distance  be- 
tween points  becomes  considerable,  as,  for  example,  in  the  electric  line 
between  Chicago  and  St.  Louis,  extended  computations  are  reqiiired 
which  involve  the  methods  of  geodesy.  Johnson's  Surveying  gives 
full  details  regarding  these  problems,  and  a  more  special  book  for  the 


164  APPE^DIX. 

obstTver  is  Doolittle's  Treatise  on  Practical  Astronomy  (third  edition, 
G4ll  pages,  $4),  wliicli  is  well  known  as  a  standard  among  geodesists. 
The  computation  of  geodetic  latitudes  and  longitudes  will  often  be 
found  necessaiy  in  this  connection.  These  are  set  forth  in  fullest 
detail  in  the  papers  of  the  United  States  Coast  and  Geodetic  Survey, 
but  they  may  also  be  seen  in  Menlman's  Geodetic  Sm-veying  (1892, 
octavo,  170  pages,  $2).  For  the  adjustment  of  precise  observations 
MeiTiman's  Method  of  Least  Squares  (sixth  edition,  198  pages,  octavo, 
$2)  may  be  quoted  as  a  well  known  standard  text-book.  Wright's 
Adjustment  of  Observations  (octavo,  437  pages,  $4)  is  a  thorough  work 
for  special  geodetic  triangulations. 

BRIDGES  AND  ROOFS. 
The  computation  of  stresses  is,  of  course,  the  first  part  in  the  in- 
vestigation or  design  of  a  bridge  or  roof  truss.  The  fii-st  treatment 
of  this  subject  was  given  in  1847  by  Squire  Whipple,  and,  twenty-flve 
years  ago,  his  book  and  one  by  Herman  Haupt  (revised  edition.  1871; 
208  pages,  with  16  plates,  $3.50)  were  the  only  ones  by  American 
authors.  To-day,  however,  there  are  a  large  number  from  which  a 
choice  can  be  made.  Du  Bois'  Strains  in  Framed  Structures  (eighth 
edition,  over  500  pages,  quarto,  $10)  is  one  of  the  most  comprehen- 
sive, including  not  only  computation  of  stresses,  but  the  discussion 
and  designing  of  details,  and  the  preparation  of  working  drawings. 
Greene's  Roof  Trusses  and  Merriman  &  Jacoby's  Graphic  Statics,  give 
methods  of  determining  stresses  on  the  drawing  board  which  will 
be  foimd  especially  advantageous  for  roofs.  Biut's  Stresses  in 
Bridge  and  Roof  Trusses  (475  pages,  octavo,  with  13  plates,  $3.50) 
is  a  valuable  contribution  to  the  subject,  and  the  seventh  edition 
contains  an  appendix  on  cantilevers.  Foster's  Wooden  Trestle 
Bridges  (quarto,  150  pages,  38  plates,  150  cuts,  $5)  Is  a  practical 
book,  showing  trestles  of  all  kinds,  which  also  treats  of  methods  of 
erection,  protection  against  accidents,  and  gives  munerous  standard 
specifications.  We  find  announced  as  in  preparation  a  work  on  Framed 
Structures  by  Johnson,  Bryan  &  Tumeaure.  and  also  a  volume  on 
Bridge  Design  by  Professor  Meniman,  which  will  fonn  Part  HI.  of  his 
Text-Book  on  Roofs  and  Bridges  (Part  I.,  Stresses,  $2.50;  Part  II., 
Graphic  Statics,  $2.50). 

CONSTRUCTION  AND  OPERATION. 
Baker's  Masonry  Construction  (sixth  edition,  550  pages,  octavo.  $5) 
takes  high  rank  as  a  valuable  theoretical  and  practical  book,  treating 


APPENDIX.  165 

not  only  of  stone  work,  but  also  of  the  important  subject  of  founda- 
tions. Berg's  Buildings  and  iStructui'es  for  American  KaUi-oads  (500 
pages,  G91  cuts,  quarto,  $7.50)  is  a  work  just  published,  which  must 
necessarily  be  in  the  Ubraiy  of  every  raUi-oad  designing  engineer,  in- 
cluding as  it  does  the  details  of  the  construction  of  buildings  of  all 
kinds  from  watchmen's  shanties  to  large  tenuuial  passenger  stations. 
Byrne's  Highway  Construction  (OSU  pages,  octavo,  $5),  Meyer's  Modern 
""  Locomotive  Constiiiction  (ti5S  pages,  1,030  outs,  $10),  Thm-stou's 
Materials  of  Coustructiou  (705  pages,  octavo,  177  cuts,  $5),  Heilug's 
Recent  Progress  in  Electric  Hallways  (12mo,  389  pages,  104  cuts),  Mar- 
tin &  Wetzler's  Electric  Motor  and  Its  Apphcation  (quarto,  315  pages, 
353  cuts),  and  American  Practice  in  Block  SignaUng  (72  pages,  small 
quarto,  $2),  may  be  mentioned  as  recent  authoritative  books  in  the 
several  departments  of  which  they  treat.  Wellington's  Economic 
Theory  of  the  Location  of  Railways  (fifth  edition,  980  pages,  313  cuts, 
octavo,  $5)  brings  together  a  great  mass  of  matter  relating  to  constnic- 
tion  and  operation  of  railroads,  as  well  as  to  location,  the  whole 
discussion  being  with  reference  to  the  most  judicious  expenditure  of 
capital.  Drinker's  Tunneling,  Explosive  Compomids  and  Rock  Drills 
(third  edition,  1,143  pages,  19  plates,  quarto,  $25)  is  a  most  valuable 
histoilcal  and  descriptive  practical  book.  Wegmann's  Masoniy 
Dams,  Men-iman's  Retaining  Walls,  Carpenter's  Manual  of  Experi- 
mental Engineering,  Thurston's  Manual  of  the  Steam  Engine,  Pea- 
body's  Thermodynamics,  Wilson's  Steam  Boilers,  Wood's  Compound 
Locomotives,  Forney's  Catechism  of  the  Locomotive,  Pai*son's  Track, 
Clark's  Building  Superintendence,  and  Ihlseng's  Manual  of  Mining  atv 
other  books  which  may  be  considered  as  safe,  reliable  and  standard 
in  their  special  field.  Of  course,  the  Pocket-Book  of  Trautwine  is  well 
known  as  the  basis  of  every  library,  and  the  one  book  which  a  rail- 
road engineer  must  have;  now  in  its  forty-first  thousand,  it  stands  as  a 
monument  of  patient  industry  on  the  part  of  its  authors. 

HYDRAULICS. 

A  general  acquaintance  with  the  principles  of  hydraulics  is  ab- 
solutely essential  for  the  siiccessful  design  of  culverts,  piers  and  other 
stnictures  in  water.  Fundamental  principles  are  given  in  Moniman's 
Treatise  on  Hydraulics  (fourth  edition,  octavo.  384  pages,  109  cuts, 
many  tables.  $3.50),  which  is  designed  as  a  text-book  for  technical 
schools,  and  also  for  use  of  engineers.  Smith's  Hydraulics  (quarto, 
362  pages,  16  plates,  $8)  is  an  elaborate  work,  giving  discussions  of  the 


166  APPENDIX. 

coefficieuts  derived  from  many  experiments.  Nichols'  Water  Supply 
(8vo,  232  pages,  54  cuts,  $2.50)  contains  accounts  of  the  methods  oi 
ascertaining  and  seeming  the  purity  of  water,  which  is  a  very  im- 
portant matter  in  planmng  water  suppUes  for  stations  and  other 
railroad  buildings.  Fanning's  Water  Supply  Engineering,  Staley  & 
l*iei"son's  Separate  System  of  Sewerage,  and  Baumeister's  Cleaning 
and  Sewerage  of  Cities  may  be  noted  as  standard  worlcs,  covering  a 
wide  field  in  the  important  subjects  of  public  water  supply  and  sanita- 
tion. The  Manual  of  Ameiican  Water  Works,  published  by  En- 
gineering News  Publishing  Company.  New  York,  is  a  comprehensive 
cyclopedia  of  statistics  and  historical  infonnation  concerning  pul>lic 
water  supplies. 


167 

V/ORKS    OK 


Professor  Manslleld  Merriman, 


A  TREATISE  ON  HYDRAULICS. 

Fourth  edition,  revised,  8vo,  cloth $3-5° 

A  TEXT-BOOK   ON   THE   METHOD    OF    LEAST 
SQUARES. 

Sixth  revised  edition,  8vo,  cloth $2.00 

THE    MECHANICS    OF    MATERIALS,    AND   OF 
BEAMS,  COLUMNS  AND  SHAFTS. 

Fourth  edition,  8vo,  cloth $3-5° 

A  TEXT-BOOK  ON  ROOFS  AND  BRIDaES. 

Part  I.  STRESSES  IN  SIMPLE  TRUSSES.  Third 
edition,  Svo,  cloth , $2.50 

Part  II.  GRAPHIC  STATICS.  Third  edition,  Svo, 
cloth $2.50 

Part  III.    BRIDGE  DESIGN.     (In  preparation). 

RETAINING  WALLS  AND  MASONRY  DAMS. 

1892,  8vo,  cloth $2.00 

INTRODUCTION  TO  GEODETIC  SURVEYING. 

Including  Figure  of  the  Earth,  Method  of  Least  Squares 
and  Field  Work  of  Triangulation,     Svo,  cloth $2.00 

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